Second-half goals from Alexis Sanchez and substitute Olivier Giroud boosted the Gunners' top-four hopes as well as ending a run of five winless Premier League matches at the St Mary's Stadium - claiming their first top-flight success there since December 2003.
They sit just three points behind Manchester City in fourth place, andWenger was pleased his side backed up their performance in beating United on Sunday.
Arsenal midfielder Mesut Ozil has told Sky Sports he gives "no worth" to the criticism he receives from pundits, and that manager Arsene Wenger's opinion is the only one that matters to him.
"We had some chances in the first half, it was a very even game". "He is always tricky to stop, very good in a short space once he has the ball in the box".
"It's hard for me at the moment, it's between [Danny] Welbeck and Giroud and both played well and have a great spirit".
Under-fire Arsenal boss Arsene Wenger has constantly reiterated his side can not put a foot wrong in their remaining games, and they were solid enough to take home victory from the south coast to keep them in the hunt for Champions League qualification. "I'm happy. Arsenal belong as one of the best clubs in the world and London is a great place to be, a great city to live in".More news: Flanagan Backs Varadkar To Be "Courageous" Fine Gael Leader
"I don't know more than you", said the Frenchman, who is still to announce whether he will remain at Arsenal beyond the end of the season. We did well being patient in the first half.
"That's Alexis", Wenger said. "You can see that the team is together, fights and is ready for it and we have to recover now physically and see how everybody is for Saturday and see do I need to make some changes".
Ahead of the game, Arsene Wenger has been speaking to Arsenal.com and he's offered a team news and injury update including the latest on Laurent Koscielny and Alex Oxlade-Chamberlain.
Every game we try to give ourselves a chance.
Under-fire Wenger has constantly reiterated his side can not put a foot wrong in their remaining games, and they were solid enough to take home victory from the south coast.
Sanchez netted his 20th goal of the season. It's a good team, a team that likes to play. They now have two games in hand on third placed Liverpool, so can make up ground on them here.