Andy Webster’s 77th-minute own goal was all that separated the sides on a night of pulsating action at Tynecastle.
The Jambos now face an uphill struggle to rescue the tie, but McGlynn insists his men can travel to Merseyside with their heads held high and with a point to prove.
He said: “The least we deserved was a draw. The effort, discipline and way we went about the game was excellent.
“It was cruel to lose that goal even if it was an excellent ball in.
“The defender was scared to leave it and then he couldn’t get out of the way of it. But apart from that Webby was superb.
“There are a lot of positives to take. It’s only 1-0 so you never know next week.
The defender was scared to leave it and then he couldn’t get out of the way of it. But apart from that Webby was superb
“If we can win at Aberdeen on Sunday we can then go to Anfield with confidence.
“We have nothing to lose as we are out of it as it stands. We won’t go gung-ho, we have to be disciplined, but we have to aim to play like this again.
“We owed the fans a performance after last year’s European game against Spurs and we gave them it. I thought we were a threat and the crowd played a part in that – Liverpool realised they were in a game.
“You can say Gerrard and Suarez weren’t playing but Henderson cost £20million and I could go on. The players should be proud.”
Pool boss Brendan Rodgers reckons his team can now finish off the Jambos at Anfield after a few scares at Tynecastle.
He said: “It’s a good win for us. In the first half we showed some good moments but in the second we were much better.
“Hearts were an excellent side and the atmosphere was fantastic.
“It was good to get a win and now we want to finish it off next week.
“I thought our passing and movement was very good at times. All round it was a good win.
“I always believed that by passing and moving the goal would come.”