Having failed to pick up a victory in their last four games, the Gunners produced a dominant display against the Eagles to collect all three points and move five points behind the Premier League's top four.
All four of Arsenal's goals came inside the opening 22 minutes, however, and Wenger expressed some regret that his side were unable to extend their advantage - while also conceding - in the lengthy period of football that followed.
"Overall we played our real game in the first half - good pace, good combination and we created great chances," he told reporters afterwards. "In the second half the challenge was to keep the same drive and we didn't manage to do that, but I'm happy we won the game.
"Crystal Palace were on a strong run and have only lost last twice in the 12 games, both against us. The speed of our game was good. They gave us less room in the second half, they didn't give up, so credit to them, they reorganised and gave us less room, and maybe we had less urgency in our game.
"The challenge [for the top four] is very difficult, but exciting as well. It will demand that we push ourselves in every single way. We have to put the effort in every game. I cannot fault the team for effort. The level of performance that will be demanded is extremely high."
Next up for Arsenal is the decisive second leg of their EFL Cup semi-final with Chelsea on Wednesday evening.