Despite their Champions League win over Barcelona, Celtic are reeling after Saturday's 1-0 defeat at home to Inverness, with manager Neil Lennon critical of his side's domestic form and threatening to quit after an altercation with supporters.
McGlynn does not believe Lennon is under additional strain at Parkhead and is ready for a similar reaction to when Celtic were narrowly beaten in Barcelona and lost to Kilmarnock the following weekend, before bouncing back with an emphatic 5-0 midweek win over St Johnstone.
"I don't think he's under any pressure," McGlynn said.
"Celtic are doing the best they've probably done in the Champions League ever; they've picked up more points than anyone would've expected.
"If they've maybe taken their eye off the ball a wee bit in defeats like Saturday, they end up coming out on the Wednesday night and in one of those situations taking five goals off St Johnstone.
"Sometimes it just takes a wee kick up the backside to bring you back down to earth.
"There's been a reaction to their defeat which will certainly have them fired up.
"When they come to Tynecastle they know they have to be at the top of their game. (The Inverness loss) will reinforce that.
"That's something we have to be very aware of and be prepared for."