Cora wasn't thrilled after Stroman - known for his demonstrative nature on the mound - tossed an apparent quick pitch against Red Sox rookie second baseman Michael Chavis in the fourth inning.
"I was telling (home plate umpire) Alan (Porter), if he's going to get on our guys, get on him," Cora said, according to Keegan Matheson of Baseball Toronto. "It's the same thing with him every day. He competes a certain way and people don't like it.
"It seems like whenever a team comes in, somebody screams at him. I don't know, that's the way he acts."
Chavis and Boston ace Chris Sale also appeared to direct some words at Stroman during the contest, but the Jays pitcher didn't seem bothered by the exchange following the game.
"Don't know (what Sale said), could care less," Stroman told Ben Nicholson-Smith of Sportsnet. "That was between me and (Chavis). That's it. I could care less what anybody else says."
Stroman threw six innings of one-run ball and now owns a 2.81 ERA in 2019.
"That just tells me my stuff is exactly where I thought it would be," the 28-year-old said. "My stuff's nasty right now and there's times when I lose it because almost it's too nasty and I can't find the zone with my sinker.
"I'm not scared to face anybody at any time and I'm able to bear down and make big pitches in big moments."
On Wednesday morning, Stroman took to Twitter to address the issue, clearly in jest:
The Blue Jays and Red Sox have two tilts left to play in their four-game series.