The Gunners have struggled with their now traditional November jitters in recent weeks after three consecutive draws.
Stalemates in the Premier League with Manchester United and Tottenham were followed by a 2-2 draw at home to Paris Saint-Germain in the Champions League this week.
However, they got back to winning ways on Sunday to move to within three points of league leaders Chelsea.
Forward Alexis Sanchez opened the scoring against the Cherries before Callum Wilson levelled from the penalty spot. Further goals from Theo Walcott and Sanchez ensured Arsenal kept pace with the rest of the title contenders and Wenger was happy to see his side get into their groove on occasions.
He told reporters: "In patches, it's always a different game after CL, mentally it's so demanding. The players questioned themselves after a few draws.
"We got better during the game but Bournemouth played well. They started with high intensity physically and when I saw that I thought they would drop a little bit in the second half.
"After that we were a bit unlucky because I think there was a second penalty on Sanchez and the penalty for them is another questionable one. After that, we had to improve our level in the second half and we did."