Although Alexandre Lacazette pulled one back, Jesse Lingard netted a third for United.
"I think we didn't start well at all at the back and we are guilty of that", Wenger, who has won only twice in 19 clashes with United's manager Jose Mourinho, told reporters.
The Frenchman deservedly received a straight red card and will miss three games, including next week's derby against City.
Two goals from Jesse Lingard and one from Antonio Valencia earned United the victory - Mourinho's first away against a top-six club since he arrived at Old Trafford. I don't know so many in English but awesome, phenomenal, fantastic.
"He is very frustrated because everybody knows that Paul is a clean player and it was not his intention at all to be close to a red card".
"We played well but there is nothing more frustrating than when you have that quality of performance and nothing to show for it at the end. But you can not make the mistakes we made at the beginning". I leave for you that one.
"The grass is absolutely attractive - I think there is a desire to go onto the grass". We were too on the edge mentally maybe - you can not be in a game like that. "I am proud of their commitment and attitude, I feel sorry for the players that gave so much". United managed to go two up within the first fifteen minutes and though the scoreline finished with them ahead on a comfortable two-goal lead, the actual match itself saw them be on the receiving end of some serious pressure from their London-rivals.
"There were fantastic individuals performances and collectively we were very strong".
Until Pogba's dismissal, everything had looked flawless for United, for whom David De Gea was outstanding and was beaten only by Alexandre Lacazette just after the interval. The Ecuadorean quickly drove forward and exchanged passes with Paul Pogba.
But this has been the most remarkable week for the 24-year-old midfielder.
"Of course, they can say they had chances but we fought and we had a great goalkeeper too and I think we deserved it".
"You need the keeper to be there for you when the team needs", added Mourinho.
"That really set us up in a place which can be really intimidating, because Arsenal are known for their fast starts".
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