Cochrane, who scored in Hearts’ 4-0 win over Celtic in December, suffered a collarbone injury when Brown landed on top of him after competing for a bouncing ball during Celtic’s 3-1 victory on Tuesday night.
When asked whether 16-year-old Cochrane should get more protection from referees, Levein said: “I think everybody should get a little bit more protection from Scott Brown.”
The former Scotland boss added: “I was annoyed about that. I watched it back and I think Scott, after the game at Tynecastle when Harry bossed him, I think he decided he wasn’t going to let that happen.
“Listen, I’ve known Scott for a long time and he’s aggressive in the way he plays, but...”
Hearts are still assessing how long the teenager will be out.
“I don’t know but he’ll certainly be out for the next two or three matches by the looks of things,” Levein said ahead of Saturday’s Ladbrokes Premiership encounter with St Johnstone.