Midfielder Stevenson was shown a straight red card by referee Willie Collum for a 25th minute challenge on United winger Gary Mackay-Steven which left the Jambos facing an uphill struggle.
And McGlynn said: "The sending off killed the game, and it was probably a very good game for 25 minutes or so. 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 [Collum] says that he never touched him but that is the rulebook and he has to go with the rulebook."
He added: "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."
Meanwhile, 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.
"When we passed it quickly we really hurt them. Mackay-Steven had three of their back four booked from running at them today so we have good talent there and confidence. The only thing I was disappointed today was not getting a clean sheet."
McNamara felt his side could have made more of having the extra man at their disposal. He said: "I thought we were guilty of overplaying in the wrong areas at times. Sometimes we took too many touches on the ball which didn't help.
"But overall I'm happy with the result which means we've got two home wins. I think we can look forward to playing Celtic away next week. Hopefully they will be a bit tired from playing Juventus during the week.
"We have the players to beat anyone on our day and that's what we have to think of going into any game. When the team is sitting in it's important they do that. We're in the top six now. We set targets where I think we should finish so we have to aim high."