Arsenal took the lead in controversial fashion 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, who lost twice last week to halt their fine start to the season, never really recovered from the sense of injustice and there was no way back once Arteta converted from the spot again on 64 minutes after Chris Brunt had tripped Alex Oxlade-Chamberlain - which Clarke felt had come following a foul by the midfielder on Goran Popov in the build-up
"There was zero contact, it wasn't even close. I am not sure what the referee saw," said the angry West Brom manager.
"It was a bad decision for us and obviously changed the shape of the afternoon.
"It could have been a nervous afternoon for Arsenal, at 0-0 they hadn't created too much.
"We knew the longer the game went the more pressure would come on Arsenal and then we would have a chance. That decision changed it."
Clarke continued: "The second was a clear penalty, no complaints, Chris fouled Oxlade-Chamberlain - but Goran Popov was fouled in the lead up to it and for some reason the referee, who gave soft free-kicks all afternoon, decided not to give that one.
"Another poor decision for us, you can add the [Per] Mertesacker handball in the first half - it was a normal ball into the box and somehow the officials decide it was a free-kick as it's the easy way out.
"They gave it for a free-kick on somebody but I've seen the replay and for the life of me cannot see a free-kick."
Clarke stopped short of calling Cazorla a cheat, though, adding: "There is a share of culpability, but on that one it is so clear there was no contact, the referee has to be better with his decision.
"I don't want a witch hunt on referees, in his country we have fantastic referees and a fantastic group that work hard to make the game the game it is.
"We have to try to work as hard as we can with the referees, in this game unfortunately it was the poorest of a really good group.
"We have a number of good referees, we have to find good more referees. that is the way forward."
Arsenal manager Arsene 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."
England midfielder Jack Wilshere produced a composed display and was the heartbeat of the Arsenal side.
Wenger said: "Jack is getting closer to the player we know he is and today [Saturday] I think he made a big step.
"You could see it already this week in training, that he has gained a little burst again, a little zip in the first three or four yards.
"In football, you have sometimes to be patient. He can only gain it by playing but of course in the first games you cannot be at that level."