Wenger saw the Gunners win 1-0 at West Ham thanks to Robin van Persie's first-half strike and said: "We had a bit of apprehension because we lost here last season and this was a big test.
"Unfortunately we didn't get that but we deserved it."
Wenger added: "There's room for improvement but I am very proud of what the team is achieving at the moment.
"I believe we can challenge. We are very young, but we have to show we can eke out results.
"Everywhere we go we try and play and improve - today was a bit different because West Ham made it hard for us to do that.
"We had a lot to deal with in the air and with the second ball, so it was important for us to keep the pace of the game high.
"We did that in the second half and I think that shows the team is maturing tactically."