The Jambos boss has been singled out for blame since last Saturday's 3-0 home defeat to Kilmarnock.
Paul Heffernan's hat-trick ensured a miserable day for a youthful Gorgie side, but McGlynn claims fans need to back off while he strives to blood a crop of teenagers.
The Tynecastle manager has been forced to introduce youngsters like Billy King, Fraser Mullan and Callum Tapping after losing stalwarts such as Ian Black, David Templeton, Rudi Skacel and Craig Beattie just as he was taking over from Paulo Sergio in the summer.
Andy Driver was the latest player to leave after joining Houston Dynamo on loan ahead of a permanent switch to MLS in the summer, and McGlynn has appealed to supporters to consider these facts before rushing to criticise him and his team.
The manager, speaking ahead of Saturday's Scottish Premier League meeting with Inverness at Tynecastle, said: "Anyone who feels they've paid their money and want to vent their anger and frustration are entitled to do that. That will happen - it goes with the territory.
"But if you're realistic and take everything on board at what's happened here and where we're going, trying to bring younger players through and get them to gain experience to handle these situations, then it is a learning curve based on the future.
"You have to remember that as well and give everyone an opportunity. It shouldn't necessarily be all or nothing at 10 to five on a Saturday night. You have to look at the longer and bigger picture and what we're bringing through here.
"It's only two or three weeks ago that all these young players were the best thing since sliced bread and all of a sudden it's going the other way.
"Football's like that. Should it be in the circumstances we're having to work under at the minute? Some will still be critical of me and others will perhaps understand the situation. Football revolves around different opinions from people."
Hearts will face St Mirren in the Scottish Communities League Cup final on March 17 as they prepare for their second successive Hampden decider.
But McGlynn says fans must accept that the Scottish Cup winners are no longer the same side.
He said: "You get to a Cup final and everyone thinks you're a great side and you should just go out and beat everyone.
"We're going through a massive transitional period which will continue into next season with players going and others coming in until it settles down completely.
"There's a lot of hard work going on trying to bring younger players through and get them the experience and continue to try and get results. We're probably no worse off in terms of being x amount of points behind the teams second and third in the league.
"But who was Hearts top scorer last season? Rudi Skacel. Who was second top scorer? Andy Webster with four goals. Andy's not scored his four goals this season. And we're missing Skacel's goals.
"That's basically the difference. Our second top-scorer hasn't scored four goals. We've not got the goals Rudi Skacel got us. We've not got Ian Black to produce that ball. Or Stephen Elliott. Or Craig Beattie. Or Suso Santana.
"It's not rocket science. There has to be a wee bit of realism here at what's actually going on. I think a lot of people do and it will be a minority who don't want to understand the situation.
"We're 90 minutes away from giving the fans the success they want in an incredibly difficult season. It's unbelievable difficult. Yet we could possibly won back-to-back Cups - it's 50 years since Hearts won the League Cup.
"I still don't know the last time Hearts won trophies in successive seasons.
"We're one game away. And it's a difficult, difficult season. We could still be in the top six.
"Hearts won the Cup with players I've unfortunately not had the pleasure to work with. We've lost our captain Marius Zaliukas, Danny Grainger too. We've not had the use of Jamie Hamill. We've lost David Templeton, Ryan McGowan and now Andy Driver.
"No club would be able to compete at the same level losing that amount of players. And players who are inexperienced at this level will become unstuck in situations like last Saturday."