The Scot insists he would have a word with any Baggies player he saw going to ground as easily as the Spaniard, who earned Arsenal a controversial penalty on Saturday
Cazorla tumbled to the floor despite not appearing to have been touched by West Brom captain Steven Reid, and Mikel Arteta scored the resulting spot-kick to put the Gunners ahead.
Clarke was critical of referee Mike Jones' handling of the incident, but stopped short of criticising Cazorla.
"I don't speak about players from other clubs," he told the Independent.
"But if one of my players goes down with something similar to Cazorla, then we'll talk about it."
West Brom defender Liam Ridgewell was accused of diving to win a penalty in the Baggies’ 4-2 victory over Sunderland back in November, and Clarke admits he has spoken to his player.
"I've spoken to Liam on a number of occasions this season," he added. "We spoke about a number of different incidents.
The Baggies defender Steven Reid, who conceded the penalty, is adamant he made no contact with Cazorla, and admits he was puzzled at the referee's justification of his decision.
"No [I didn't touch him] and looking back at the replays even more so," he told BBC Radio 5live.
"You'd like to think that even if there was a graze of a sock that's still not enough to go to ground. Even if it was that, which it wasn't, it's disappointing.
"I might have had a little chat with Cazorla when I was waving a finger but I'm not sure I can repeat it as it wasn't too friendly.
"He almost looked a little embarrassed afterwards.
“I said to the referee there was no contact and he pretty much said that the intent was there, which I found a little bit strange."