The Gunners took the lead midway through the first half as Spain midfielder Cazorla flung himself to the floor following a challenge by Steven Reid, with replays showing there was no contact. Mikel Arteta converted the resulting penalty.
The Baggies never really recovered from the sense of injustice and there was no way back once Arteta converted from the spot again after 64 minutes after Chris Brunt had tripped Alex Oxlade-Chamberlain.
Wenger had not reviewed the incident but revealed Cazorla insisted there had been contact.
"I am sorry if it was not a penalty but I have spoken to Santi and he said he was touched, lost his balance. Has he made a bit more of it? I don't know," Wenger said.
"When he [a player] is touched, he goes down, the referee can give or not give the penalty.
"Of course [I will speak to Santi if he has not been touched]. I will look at it, don't worry."
Despite its controversial nature, it was a much-needed first victory in four matches for the Gunners, who have moved back up the Premier League table as a result.
"Overall we played well. We were maybe a bit lucky on the first penalty but we created chances and kept a clean sheet," Wenger said.
"We have shown a great spirit, which many people questioned after our last game, so we did our job very well. You could feel we were ready for a fight and that we absolutely had to win this game, which is what we did."