McGlynn believes some are taking great joy from "booting" Hearts over their perilous financial state, which saw them avert a tax-related winding-up order before Christmas and has been further clouded by the descent into administration of owner Vladimir Romanov's Lithuanian bank.
McGlynn faced criticism from some fans after his side's 3-2 home defeat by Inverness on Saturday, which left them eight points off the top six of the Clydesdale Bank Premier League ahead of tomorrow night's clash at St Mirren Park.
And the Tynecastle manager - who has warned that this season is all about the club's survival, despite next month's Scottish Communities League Cup final against the Paisley side - wants supporters to focus on external battles.
McGlynn said: "I think it's the same as Rangers last year, when you are down people just boot you. That's how it goes and I think Ally McCoist went through that as well.
"That's why I would appeal to the Hearts fans to stick together and let's fight against all the other teams that we have got to compete against.
"We have enough battles out there with everyone else without having to battle against ourselves."
McGlynn declined to specify on the perceived persecution, saying he did not want to "go too far", although he admitted the club's previous spending policy was coming back to haunt them.
He said: "We have brought it on but it's easy, it's the same with Rangers last year, everyone loved just booting them.
"They probably felt we overspent, which might well have been the case."
The former Raith Rovers manager added: "If you start winning football matches, it helps. That's the thing that makes the doubters go away.
"It's not that simple because of the circumstances but the longer-term future is very, very bright and the players are picking up massive experience."
McGlynn believes most Hearts supporters appreciate the constraints he is facing - five teenagers and five other players aged 22 or under played against Inverness on Saturday.
"There will always be a minority who will be unrealistic but that's par for the course, it doesn't matter where you are," he said.
"I think the majority of fans realise that not long ago there was a winding-up order and they could have lost their football club.
"In some ways that's what it is going to be this season, to get by and regroup in the summer and kick on again.
"We all want to win cups and we are not far away from winning a cup. We all want to be in Europe, of course we do.
"A lot of football people realise I'm having to put young players in. It's a really good style of football and it's pleasing on the eye.
"I think people recognise that we are trying to play good football and the younger players have come through with a philosophy to pass the ball.
"That will make us better in the long term."