Stevenson was dismissed for a 25th minute challenge on United winger Gary Mackay-Steven.
"The sending off killed the game," said a disappointed McGlynn.
"The players feel if you go into a tackle when you are on the ground you can hardly go with your studs on the ground."
McGlynn conceded that he did not have a very good view of the incident and said the club would review video evidence before deciding on an appeal against the red card.
"The few people I have spoken to who have seen it on TV think it was harsh," explained the Tynecastle manager.
"We will have a look at it once we get some video coverage but it didn't help us today.
"According to Ryan, the lad [referee Willie Collum] says that he never touched him but that is the rulebook and he has to go with the rulebook.
"It is hard enough losing a player for an experienced side to cope with but we're not an experienced team.
"We had a lot of young players out there today so it was hard going.
"We gave ourselves a chance through Michael Ngoo's goal late on but I can't fault the players too much for their effort."
United boss Jackie McNamara agreed with McGlynn that Stevenson should not have been dismissed, after seeing goals from Johnny Russell, Willo Flood and Michael Gardyne make Ngoo's 76th-minute strike a mere consolation.
He said: "Obviously it helped us more in terms of 11 v 10 but it didn't help the spectacle of the game.
"I thought it was harsh but I would need to see it again."
Hearts had suffered an earlier blow in the 19th minute when skipper Marius Zaliukas was forced to go off injured after clashing with Russell and then appearing to land awkwardly on his ankle.
"To lose a goal inside a couple of minutes was not the start what we were looking for, obviously," said McGlynn.
"Then we lost our captain and went a man down; not much more could have gone against us."
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