Arsenal striker Danny Welbeck scored twice as they were comfortable winners against Bournemouth.
Welbeck opened the scoring early on with a mistimed header before setting up Alexandre Lacazette and then completing his brace with a well-taken second.
Wenger said: "Yes I'm pleased with the win and the way we played. It's always a test when you have such a negative experience, like we had, for the mental health of the team to respond. We had a committed, disciplined and a very good offensive performance.
"I believe in my players. Our two away games… At Stoke we played quite well. We had plenty of chances and were a bit unlucky at Stoke because we had 75 per cent possession and we didn't deserve to lose the game. At Liverpool, we had a terrible performance."
On Danny Welbeck, Wenger added: "He gets stronger and stronger. Let's not forget that he was out for a long time. He gets stronger and stronger. He's a team player, Danny Welbeck, and that's why coaches love him.
"He's a guy who has a huge physical potential. People are not convinced that he is a great finisher, but these kinds of goals will help him become more relaxed in front of goal. I liked his second goal today because it was the clean finish of a goalscorer."