A big crowd had turned up to see Glasgow's first PRO12game at the revamped Scotstoun Stadium but the Warriors couldn't come up with a performance to match.
Gregor told the Scotsman: “To lose on such a big occasion like this, and when we believe it was so much of our own doing, is very hard to take.
“We had 21 turnovers compared to the opposition's 13 and that's going to put you in a very difficult place to win. It is very frustrating. We're here to win and we haven't won our first two games. We're here to improve and win. That's all we're here for and we'll be working even harder to achieve that.”
The Warriors will be back in for training tomorrow and skipper Alastair Kellock admitted they have to improve quickly before next week's trip to face Ospreys, saying: “Too many mistakes killed us.
“They didn’t have to do much. It was a similar story to last week in that we gifted them tries and when we had the ball we knocked it on, gave forward passes, ran isolated, kicked the ball dead and did all sorts of things that you just can't do.
“We’re not where we need to be. This was a massive occasion and we were focused on the rugby. The biggest point we've made is that what we’ve done in the past has got us this place, and what we do now earns it, and so far we’ve not earned it.”