Hearts finished the match with 10 men after Scott Robinson was sent off but they held on to get to, and get through, extra-time at 1-1 and when Philip Roberts missed from the spot they were able to celebrate their final place.
The win is sure to give the cash-strapped club a very handy financial boost and will be put a smile on their fans' faces after a season that has been full of turmoil
"It's massive," McGlynn said. "It's a great boost for the fans because there has been a lot of doom and gloom this season.
"There has been a lot of negativity, and hands up, a lot we have brought on ourselves. But nevertheless it's great for the fans to go back to Hampden.
"It was great here, they must have seen the fight in the players. How Inverness didn't score the opportunity when it was two against one was partly their fault but our players had the fight to get back and stop the ball going in the net.
"We had seven U21s on that park, five of them came through our youth system, and other players over 21 who came through our youth academy.
"So we owe a big thanks to everyone who has worked in our youth system. Financially it's a massive boost as well because the football club is not out the woods yet."
"I'm very proud of the performance and the fight of the players today. It will be a special, special occasion to do that (go to Hampden). That's why I came back to Hearts, they are a team over the past 100 years who are fighting for third in the league and involved in semi-finals and finals.
"That's part of why you follow Hearts and come back to Hearts to be part of that and I'm delighted after seven or eight months that we are going back to