A first-half goal from Granit Xhaka and a penalty after the break from Pierre-Emerick Aubameyang were enough to condemn the Red Devils to just their second defeat in all competitions under Solskjaer, and their first in the Premier League since he took over.
Speaking after the game, Solskjaer said he was more disappointed with the profligacy of his players as opposed to the team's overall performance, per Sami Mokbel of the Daily Mail.
"It has been fantastic so far, but today is the lowest we have been because we lost and missed the chance to put pressure on Spurs," he said. "We have won games we have not deserved to win, and today we lost a game we did not deserve to lose."
Solskjaer was critical of referee Jon Moss for awarding the Gunners a penalty after the break, with Alexandre Lacazette going to ground in the box after a second-half challenge from Fred.
"I don't think it is a penalty. That is a decision the ref had to make, but Jon Moss might be disappointed when he sees it again," he said. "I don't think there's enough contact there to warrant a penalty."
The United manager also told Sky Sports his players may have been feeling the effects of their UEFA Champions League win over Paris Saint-Germain on Wednesday:
Sky Sports Premier League @SkySportsPL
"Maybe a backlash from Wednesday night." 🤷♂ Ole Gunnar Solskjaer reacts to his first domestic defeat as @ManUtd manager, saying his side played better today than when they beat @Arsenal in the FA Cup. Match report and highlights: https://t.co/9pVMTZ5AFz https://t.co/QCx74DEEl3
Following on from the defeat, which saw the Red Devils slip out of the top four at the expense of Arsenal, Statman Dave sought to put the record of Solskjaer into context:
Overall, United didn't perform badly at the Emirates Stadium, as the match was on a knife edge for long spells.
Xhaka's effort from long range wrong-footed the usually impeccable David De Gea, and the penalty award was controversial. In addition, the visitors let a number of big chances slip by, with Romelu Lukaku in wasteful mood; both he and Fred hit the woodwork with first-half strikes.
Still, the fact United even find themselves in a position to be competitive in the top-four race, not to mention in the last eight of the Champions League, is testament to Solskjaer.
Football writer Daniel Storey said Sunday's performance is not something to be concerned about:
James Robson of the Evening Standard said a lot went against the team:
United's season is still alive. Not only do they have a top-four berth to battle for, they will be dangerous in European competition and are also in action in the quarter-finals of the FA Cup on Saturday, when they visit Wolves.
Solskjaer would have learned plenty from Sunday's match, and losing at the Emirates is not something to get too disheartened over.