United had won all nine of their away matches under Solskjaer until their trip to Emirates Stadium, where goals from Granit Xhaka and Pierre-Emerick Aubameyang struck a potentially telling blow in the top-four battle.
Xhaka opened the scoring after 12 minutes with a swerving shot from 30 yards out that bamboozled David de Gea, while the visitors twice hit the woodwork before half-time.
The Red Devils failed to make their pressure count early in the second half and the result was put beyond them when Aubameyang converted from the spot after Alexandre Lacazette went to ground under pressure from Fred.
Solskjaer was unhappy with the penalty decision but said his players ultimately let themselves down with a sluggish first few minutes, only four days on from their dramatic win at Paris Saint-Germain in the Champions League.
"We started slow," he told Sky Sports. "Maybe it was a backlash from Wednesday. We created chances – when they get the first goal, it's a different game.
"We created so many more chances compared to when we beat them in the [FA] Cup. We played a better game than we did back then, but that doesn't help when the result is like this.
12 - Arsenal have won 12 points in their 10 Premier League games against fellow 'big six' opposition this season - double the amount they won in such games last season. Improved. #ARSMUN pic.twitter.com/JbV6nSmg7f— OptaJoe (@OptaJoe) March 10, 2019
"It's not scratching your head. Sometimes it happens. We hit the woodwork twice, we got four, five very big chances. Some days, strikers take them; some days, they don't.
"I can't remember any saves that David had to make, proper saves. Of course, the penalty – I think the referee will be disappointed when he sees this, I don't think it's a penalty. They didn't really carve us open."
Solskjaer refused to blame De Gea for Xhaka's opener, instead claiming United's outfield players should have closed the midfielder down more quickly.
"He's disappointed every time he concedes a goal because he's a top, top keeper," he said. "The ball moves so strange, and when you see it on telly, it looks like it goes to David's left and it just changes direction.
"But we were too slow, first 15 minutes, we were too slow to get up to them, we never put them under pressure and he had time to hit that ball.
"It's one of them where we weren't really at it. One of those days you have to dust yourself down, have a good reaction – we have Wolves in the [FA Cup] quarter-final and it's a good game to look forward to."
United have had to contend with a host of injury problems during a packed recent fixture schedule, but Solskjaer would not accept that Sunday's result was down to a build-up of fatigue.
"Not at all," he said. "The first goal decides how a game goes. They scored the first one and maybe let us have the ball a bit more than they wanted to.
"I thought we created some great chances, but we just didn't take them. Sometimes, as a striker, I know more than anyone that you can miss chances."