DTH van der Merwe's late try levelled the scores and Finn Russell kicked the tough conversion to earn the hosts a 16-14 victory.
Gregor told BBC Scotland: "Comparing it to last year's game in Munster, it was a top-quality performance by both teams last year. This wasn't.
"But the character in this group drove us forward."
Glasgow were second best for much of the contest and Townsend admitted it took a gutsy performance to make it through to next week's final against either Munster or the Ospreys in Belfast.
"We made too many errors and Ulster played well, but the players they worked out a way to win," said Gregor. "I can't be any prouder of the squad.
"We've got a lot of quality players here and you can tell the players who came off the bench really raised the tempo and they adjusted well to losing their starting hooker, their captain after 10-15 minutes, they did very well.
"Whatever team we can pick next week, it'll be a strong team."
DTH's try will be his last in the home colours at Scotstoun, with the winger having already signed a contract with Scarlets.
DTH said: "It was a tough game, I'm glad the boys stuck in there. Every opportunity when I got the ball in my hands, I just try to do as much as I can.
"That try was a team try, I was just lucky to be on the end of it. Finn Russell with a great pass.
"It's a quality team. Great supporters, great coaches, staff behind the scenes.
"I'm going to really miss this place, but there's definitely guys who are going to fill the void for the guys who are leaving.
"There are still great things to come from this club."