Gary Hooper and Georgios Samaras put Celtic 2-0 ahead inside 12 minutes.
Despite Jason Holt pulling a goal back in the 68th minute to create a nervy spell for the hosts, Hooper grabbed a third to make it 20 for the season before substitute Lassad Nouioui made it four in added time.
He said: "The only positive is that after being two down after 15 minutes, we had the chance to win it with five minutes left, because many teams would come here and possibly crumbled.
"It wasn't the start we wanted, to be a goal down after 90 seconds and certainly not to be two down after 15 minutes.
"It gave us a mountain to climb but at least we stuck together and got a goal back. But the two soft goals that we lost towards the end were easily preventable. We had a lot of young players and it was a hard lesson to learn."
McGlynn was pleased with defender Danny Wilson, 21, who made his debut after joining Hearts on loan for the rest of the season from Liverpool on Friday.
He said: "I thought he acquitted himself very well. He has been playing games and he will certainly be a good acquisition between now and the end of the season."