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."
West Brom boss Steve Clarke was furious after the match and insisted the referee should have spotted there was "zero contact" on Cazorla, but fellow Arsenal midfielder Arteta refused to accept his fellow Spaniard had attempted to con the referee.
"Santi was saying that he felt something. If there is a little (contact), it is (still) contact. The ref makes decisions, some right and some wrong," Arteta said.
"For me, it is not right to dive. Santi is not a player who dives. He has taken a lot this year because of the way he plays and if he has done it (it is) because he felt something and changed direction, but he is not that type of player."
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- Mikel Arteta