Ross MacIver scored in first half injury-time to make it 2-1 at the break and Liam Henderson’s header pulled Falkirk level with 25 minutes still to play.
They didn’t look content to sit back and defend their lead though, and McGlynn brought on attacking reinforcements in the form of Brian Graham, Scott Arfield and Alfredo Agyeman.
“I really enjoyed Falkirk in the second half,” former boss Ian McCall added on Sportsound. “They fully merited their point.
“The crowd sensed they were going for a winner at the end but it just didn’t happen.”
Manager McGlynn was also slightly disappointed not to come away with all three points but understands the importance of not losing the game.
“We caused them problems throughout and on another night, we could have gone ahead early on,” he said.
“We knew Hibs have a bad record of losing goals just before half time, we mentioned that to the players. The goal was the difference between us getting a point and not and getting confidence in the players to say we are very much in this game.”
Tuesday’s performance is not the only evidence of Falkirk’s fighting spirit this season.
In their defeat by St Mirren last weekend, Graham’s late goal almost sparked a spectacular comeback and in their season opener, they twice came from behind against Dundee United to snatch a point.
McGlynn’s men have won two points from losing positions in the Premiership – the second highest in the division. Only Hearts, with seven, have recovered more.
“We never fail to entertain,” the manager said. “We play good football and we go out to attack in every game.
“The atmosphere was amazing. Great mentality from the players, to be 2-0 down against a team like Hibs and to come back speaks volume for everyone involved and the fighting spirit.”