The stalemate means the Gunners have gone eight games without a win in all competitions and they now sit seven points adrift of the Champions League places.
Some big improvements are needed if Arsenal are to find a way of securing the top-four finish they crave.
At present it’s unclear how long Ljungberg will be in charge but Arsenal insist they will not rush into appointing a permanent successor for Unai Emery, meaning the Swede could be in the job for a while.
Below Goal takes a look at the immediate issues he must fix in the short term to get Arsenal firing again.
Improving the defence
This has to be the first priority. If Arsenal are to arrest their current slide they simply have to improve at the back.
Under Unai Emery, the Gunners conceded 19 goals in their first 13 Premier League games this season and they conceded a further two at Norwich.
That is not good enough for a team with ambitions of a place among the top four and continues on the trend from the past two campaigns which saw them ship 51 league goals in each.
Emery tried many things, switching from a back four to a back three and he used several different defenders along the way, but none of the combinations proved to be successful.
Ljungberg brought back Shkodran Mustafi at Carrow Road on Sunday, handing the German his first league start of the season alongside David Luiz.
That couldn’t stop Arsenal conceding twice, however, with the home side picking the Gunners off on the counterattack on two separate occasions before half-time. Had it not been for Bernd Leno, Norwich would have scored more.
“We have a problem in transitions, and that’s what I will try to fix,” said Ljungberg after the game.
If he can do that, then there is no doubt the wins will soon come given the attacking quality that Arsenal possess.
Find the right balance in midfield
As much as the defence is the major problem for Arsenal, the lack of balance in midfield contributes greatly to Arsenal’s problems at the back.
Time and time again you see teams just cut through Arsenal with ease, getting straight in on the defence and creating shooting opportunities. Leno has made 59 saves so far this season in the Premier League; no keeper has made more.
For a spell last season, it looked like Arsenal had finally landed the defensive midfielder they had been searching for by bringing in Lucas Torreira from Sampdoria.
The Uruguayan sat in front of the back line and was exceptional, but his form dipped massively during the second half of the campaign once Emery started to move him out of position.
Torreira found himself being played in a more advanced role, with Emery believing he wasn’t good enough on the ball to play as the deepest-lying midfielder because his distribution wasn’t of a sufficient standard to start off attacks.
His form suffered as a result and Arsenal have certainly missed his presence as a defensive shield ever since.
There is a lack of mobility in the midfield and neither Granit Xhaka or Matteo Guendouzi have the defensive mindset to sit deep and offer the defence protection.
Ljungberg talks about Arsenal having problems in the transition and that really is about the midfield. When they lose the ball high up the pitch, the defence is left totally exposed.
The Swede must find a way of making the team more compact so the much-maligned defence begins to get more protection than it has been receiving in recent years.
The Pepe situation
It was telling at Carrow Road that Ljungberg’s attacking substitutions saw him bring on two teenagers as Arsenal searched for a winning goal.
Gabriel Martinelli was brought on first and then Bukayo Saka followed. Meanwhile, Arsenal’s £72 million ($94m) club-record signing Nicolas Pepe remained on the bench.
That was a clear sign of where Pepe finds himself right now. The winger’s last league start came during the 2-2 draw with Crystal Palace in October.
Since then he has played 13 minutes against Leicester and 45 minutes against Southampton. He has also been an unused substitute against Wolves and Norwich.
“Pepe is a very good player," Ljungberg said when quizzed on why he didn't feature against Norwich. "But I looked at what we did in training and what I see every day and that is how I judge it.”
The winger's form is a real problem for Arsenal. He was brought in at huge expense to ease the burden on Pierre-Emerick Aubameyang and Alexandre Lacazette and so far it has not happened.
He has scored three goals and contributed four assists so far this season in all competitions. His only Premier League goal came from the penalty spot. For £72m Arsenal would have expected far more.
Pepe is better than what he has shown so far. He has struggled to adapt to English football and his confidence has clearly now taken a major hit.
But it’s not helping anyone having him sitting on the bench each week so Ljungberg needs to find a way of lifting the Ivorian and getting more out of him.
We saw last season in Ligue 1 just how dynamic and prolific Pepe can be when confident and in form. Arsenal desperately need him to start replicating the sort of performances he produced for Lille on a regular basis here.
Improving the away form
The win at Newcastle on the opening day of the season remains Arsenal’s only away success in the league in 2019-20.
Under Emery last season and Arsene Wenger the season before that, the north Londoners' away form was atrocious and that has carried on into the current campaign.
If Ljungberg has any hope of improving Arsenal’s current plight - and giving the Gunners any hope of a top-four finish - then he must get results away from the Emirates.
You can’t just rely on home form if you want to qualify for the Champions League, you have to pick up points away as well.
Ljungberg will be well aware of that and will know that if he can tighten things up defensively then Arsenal will stand a much better chance of enjoying some success on the road.
Unifying the club
Arsenal has been a divided club for some time now.
From the final years of Wenger to Emery’s short stint in charge, divisions have never been far away form the surface.
Given Ljungberg’s past, he will always be a popular figure with the fans so his main aim now will be bringing everyone together in the changing room once again.
The last couple of months of Emery’s reign took their toll in terms of the atmosphere inside the club. He had lost several of the players and the mood at the training ground became uncomfortable.
Ljungberg will obviously have been aware of that, given he was part of the coaching set-up, and he admitted immediately after his appointment that he needed to lift the mood.
“I’m here to help as much as I possibly can and try to get a good atmosphere around the club,” he said. “That's what I'm focusing on at the moment.
“For me, happy footballers play the best football. That's a part I learnt as a player, there is a time to work hard but at the same time we need to enjoy what we're doing.”
Get Lacazette firing away from home
Lacazette is a massively important member of the team and the fact he won Player of the Year last season shows how important he is.
But away from home he does not contribute enough in terms of goals. This season Arsenal have scored seven times in the league away from the Emirates and Aubameyang has scored six of them.
A player of Lacazette’s quality should be shouldering some of that burden but he has struggled to get on the scoresheet away from home since he arrived in England.
When Arsenal are at home, Lacazette consistently finds the net but the same can’t be said for him outside north London.
In fact, just seven of his 31 Premier League goals have been scored away. Since scoring twice at Fulham in October last year, the France international’s only league goal on the road came in the win at Huddersfield in February.
That’s not good enough for a striker of his ability. Ljungberg needs to find a way of getting the best out of Lacazette away from home. If he can’t, then it might be time to start exploring other options when it comes to his attack.