The first half of the season saw the Gunners embark on a 22-game unbeaten run across all competitions, but a dip in form after Christmas invited fresh criticism.
Emery's side ended up finishing fifth in the Premier League and missed out on a place in next season's Champions League as a result.
It is believed that Emery will be operating on a modest budget of £40 million ($51m) in the transfer market, with a few high-profile departures necessary to raise extra funds.
Dixon, who played for Arsenal between 1988 and 2002, has urged the club to strengthen in the current window to avoid another year of mediocrity.
“It’s a huge summer for Arsenal,” Dixon told TalkSport.
“It was always going to be a big summer regardless of where they finished and whether they got to the Europa League or not.
“I think Emery knew this season was going to end like this, to a point where we either got into the top four and got Champions League football or we didn’t quite. We failed on that front.
“So he’s got to look accordingly and try to convince the board and powers that be to give him enough money to improve the squad.
“It does need improving in all departments, and let's hope we can keep hold of our best players in order to do that.”
The Gunners have been heavily linked with a move for Borussia Dortmund midfielder Mario Gotze, but he has played down a possible switch this summer.
Bournemouth ace Ryan Fraser has also been mooted as a target, with Emery looking to bolster his options across the middle of the park after Aaron Ramsey's departure.
Danny Welbeck will follow the Welshman out the exit door upon the expiration of his contract this month, while Lucas Torreira is thought to be considering a surprise return to Italy.