United had stopped Wenger's side from achieving an unbeaten run of 50 games, recording a 2-0 win.
Arsenal, on the other hand, are fighting for a top-four place in the Premier League and need to win all their games to have even a slight chance of making the Champions League next season.
On Sanchez's well-taken goal, Wenger added: "That's Alexis, he's a player that never gives up and is tricky to stop".
Well, I wish we'd found it [good form] before. "We went through a bad patch".
"It was a hard game but we expected that and I believed in the second half we could score the goals that we didn't in the first half because we created more space. The whole team was dynamic, focused and showed a convincing desire to win the game".
"It's hard to assess now after the game", Wenger said. We know we can only win our games, and we had a strong performance on Sunday.
This victory may not mean as much as it did during the "Invincibles" campaign, but it could have long-lasting ramifications for both Wenger and Arsenal as the Frenchman continues to contemplate whether to sign a new deal.
Arsenal move up to 5th place after the win, a point ahead of Manchester United and three points behind Manchester City.
The results of the last meetings between these teams in two cases remained in favor of Southampton, twice won the Arsenal, and also one match ended in a draw. We came to a hard ground today - and another on Saturday.
Wenger confirmed former Southampton man Alex Oxlade-Chamberlain was forced off in the first half with a hamstring problem - but is hoping it was mainly fatigue for the England global.
Saints boss Claude Puel, however, was left to ponder his side's lack of a cutting edge. "But I do not know about the FA Cup final". Breaking the deadlock with a composed finish early in the second half - producing a dummy a la Mesut Ozil (also good tonight) to put two Saints players on the floor before slamming the ball past Fraser Forster. "I am always harsh with the one who doesn't play". "In the second half we took over and created many opportunities to score".
"It was interesting to play at this level against a good team", said Puel.