Arteta’s side missed the chance to go fourth in the Premier League after surrendering a lead and then losing to a Cristiano Ronaldo penalty after pegging the score back to 2-2.
Arsenal boss Arteta felt the visitors had been the better side for long spells but then paid the price for some mistakes.
Arteta said: “We scored the first and after that we had perfect control of the game but we started to give some very simple balls away in very dangerous areas.
“We gave them so much space, they gained some momentum and we had some difficulties there. We conceded the goal.
“We started the second half well and had total control but then conceded again. We dominated again and scored the second one but after that we need to have the maturity to go on and score the third one. We didn’t manage it and they scored again.
“But being realistic, conceding three goals at Old Trafford makes it very difficult to get something from the game.”
Arsenal took the lead in bizarre circumstances in the 13th minute when Emile Smith Rowe fired past a prone David De Gea.
The United goalkeeper thought he had been fouled and his team-mates expected play to stop but it transpired he had been felled by his own team-mate Fred. The goal was allowed to stand after review by VAR.
“It was a very quick action,” Arteta said. “We did not know what to expect. They allowed the goal but I haven’t seen the images again.”
United equalised through Bruno Fernandes and then took the lead with Ronaldo’s first of the night. Martin Odegaard levelled for Arsenal but then conceded the penalty that allowed Ronaldo to win the game.
Asked about that decision, Arteta said: “The VAR checked it and hopefully it was the right decision.”
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies