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 Wednesday 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."