Solskjaer was furious that Moss ruled Fred's challenge on Alexandre Lacazette was worthy of a spot-kick in the 69th minute.
Granit Xhaka opened the goalscoring for Arsenal as David De Gea committed a mistake in judging the ball.
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.
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Solskjaer has turned the team's form around since taking over in December, following the sacking of Jose Mourinho. "Laca gave me the penalty and that was cool from him, I was really focused", Aubameyang said on Sky Sports.
Arsenal return to action on Thursday night, welcoming Rennes to north London in the second leg of their Europa League last-32 tie.
Solskjaer admitted United's tame opening may have been in part caused by fatigue after their European heroics. We created five big chances, hit the woodwork twice.
Arsenal move above United into fourth place as the race to qualify for next season's Champions League gathers pace. "It was important to take the three points and now we're back in the game".
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She retired after losing the first game. "It was hard for me to close out those sets", Halep told reporters, praising Kozlova. The Romanian was one of six seeds to progress, with Svitolina joining her after a 7-5 6-4 win over Daria Gavrilova.
Even Arsenal manager Unai Emery said the decision looked generous to his side but he added that it made up for the one that went against them, and that Tottenham's Harry Kane scored from, when Arsenal visited Spurs.
"I think we could have achieved something great today and kept the win, but it's football and we have to learn".
"We knew it was one of the best teams in the league".
The Gunners are two points ahead of United and only one point behind third placed Tottenham, with sixth placed Chelsea three points adrift of the top four with a game in hand.
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"Being competitive like today for 90 minutes can give us a stronger mentality".