Second-half goals from Nacho Monreal and Gervinho gave the Gunners a 2-0 win at the Liberty Stadium and closed the gap on Chelsea in fourth to leave Wenger feeling proud of his players.
"We knew on the fixtures that this was one of the difficult games we had still to play," Wenger told Sky Sports.
"But we really wanted the win today and we kept going. The fact that our left-back scored the goal inside the box shows that we had the spirit, the desire and are up for the fight.
"I'm very proud of the players because they have given a lot at Bayern Munich on Wednesday, come home, travelled straight away and won again away from home. It's never easy to do that.
"Winning a big game like that (against Bayern), of course, improves your confidence even if it is a frustration to go out. We were up for a battle in Munich and it certainly helped."
The introduction of substitutes Aaron Ramsey and Gervinho also seemed to spur the Gunners to victory with the breakthrough coming soon after, before both men combined for the second goal.
"They had a good impact because we were starting to become a little bit tired," added Wenger.
"But overall I think the team just kept going. I think it was the team that really wanted it today that have won the game.
"We've not always had that belief that you need at this level but the players were determined to give absolutely everything."