Finn Russell was faultless with the boot, kicking five penalties in what was only Glasgow's second win on French soil in Europe's premier competition.
Gregor said: "We understood what this game meant. This was our first away game, Montpellier picked up a bonus point last week, Toulouse won today and could have been clear at the top of this group.
"We produced a huge defensive effort, and kept knocking Montpellier back, especially in our part of the field."
Gregor's playing career included time with Brive, Castres Olympique and Montpellier and he made use of that experience in Glasgow's preparations.
"This was Finn Russell's first European start. He had a very mature performance, it was only his second start of the season, coming back from injury. He had learned a lot from his last game, some of his kicking and decision making today was excellent, his composure for the goal-kicking was superb.
"We do have a lot of experience as well, with guys like Euan Murray, who had to play something like 30 scrums in 79 minutes. It's a collaboration, with players and coaches working well together.
"I sort of had an insight to the French psyche this week and what we could expect on how Montpellier would try to assert their dominance, a lot of driving mauls, pressure in the scrum.
"There were times where they had an edge, but we came back strong. We made good decisions when we had possession in the first half, and it gave us a little lead. It kept the pressure on Montpellier to do something, and they have the players to do so. But we defended really well."