The Gunners fell behind when Carlton Cole scored in the first minute of the second half but were able to return to the top of the Premier League table thanks to a brace from Theo Walcott and a goal from the returning Lukas Podolski.
After the triumph, Wenger spoke positively about his players despite a tardy beginning at Upton Park.
"Overall, I feel we controlled the game but felt we had a difficult period where the game could have changed. That was in the first 10 minutes of the second half when West Ham scored and they had a header from a cross, which could have been 2-0," he told Sky Sports.
"That was certainly the turning point of that game and after that we had plenty of chances. We couldn't take our chances in the first half and we responded very well in the second half, in the end winning the game in a convincing way.
"I have confidence in my team - I have confidence but I also worry. That is the nature of the game, you always worry.
"I am proud of the character of this team because they are always focused and try to do well. They responded, but football is football."
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