A brace by former Marseille ace Samir Nasri secured the win for the Gunners.
Wenger told Sky Sports: “I can take criticism. I am in a job where I have to accept that. There is only one answer to give, and that is the quality on the football pitch.
“It was of course vital to win. Overall, it was a great football game. Both teams really went for it.
“I knew today that was a big game for the future of the team. We needed to keep in the race and know we can win big games.
“Man United are a great side and they created chances but didn’t take them. We took our chances today.
“They took the initiative when they were 2-0 down. They scored very late and we had a nervy six minutes in the end.
“We continued to go forward. When you play football in a negative way you put yourself under pressure. We tried to score the third goal.
“We are player-ish, you know. That always takes over. When you are 19 or 20, you want to play. But overall, it was a great performance from my team.”
