Wenger believes that his team were nervous early on at the Emirates Stadium but merited the three points.
He told BBC Sport: "We came out of two massive disappointments and the team were a bit nervous but focused at the start.
"Overall, it was a deserved win and gets us again in a more serene atmosphere. It's been quite rocky in recent days. It was important to get three points today.
"The classy players do it when it matters and he (Santi Cazorla) did it today. When you come out of a crisis like we had in the last few days you might be happy with a draw but when you win you say 'thank you'."
The Gunners are now one point behind local rivals Tottenham Hotspur in the final Champions League qualifying place.