"It was massively important we got off to a winning start. We had a home fixture and if you want to do anything in Europe you have to win your home fixtures as this group is not going to be easy," said Gregor.
"Our defence really stepped up in the second half and we shut them out.
"We didn't give them any opportunity to do anything and we focused on preventing them from scoring.
"The Dragons are a difficult team to play against, they know exactly how they want to play and are very efficient at that.
Glasgow top their group after the first weekend of fixtures but face a tough trip to former European Champions London Wasps on Sunday.
"It is going to be tough down at Wasps," added the 29-year-old.
"But I think we can take a lot of positives out of this week, particularly our defence and how we stopped the Dragons.
"There are a couple of things to work on in attack, when we get into the opposition 22 we have got to come away with points, but I think we have got a good chance down there."
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