The Gunners capitalised on mistakes from Wes Brown and Vito Mannone to secure a 2-0 win at the Stadium of Light as Alexis Sanchez scored a brace to fire Wenger's side to their third win of the season.
Wenger told BBC Sport: "You could feel that we had a lot of the ball and Sunderland were focused on defending very well. They came out with more purpose in the second half but on the break we had many chances.
"We played away on Wednesday and again today so what was most important was the points. In life you can always improve but what was important for us today was to get the three points and keep a clean sheet.
"Sanchez is not scared to take the ball and go at you anywhere and that is very important. He got two goals but we want more."
Arsenal are now fifth in the Premier League table following their win over the Black Cats.