A young Jambos side dominated the game but failed to find a winner until substitute John Sutton netted against his former club four minutes from time.
"The players were a bit tired and bringing on those fresh legs got us the goal," said McGlynn. "We're delighted that we got the victory.
"I think we deserved three or four more goals. I felt we were in control of the game, but obviously we hadn't taken the chances until that point.
"In fairness to us I thought (Dundee goalkeeper) Rab Douglas had an excellent game, he always seems to have a good game against us.
"We had many young players out there on the pitch, just as we did on Saturday.
"I said when I came in that there would be no better time to be a young player at Hearts. There are more and more appearing in the team and that makes our bench more experienced because of that.
"You saw tonight we were able to turn to Sutton and Novikovas, but we also had Andy Driver, Medhi Taouil and Darren Barr. These lads will respond and it should make the whole squad stronger."