The win means Warriors are the only team with a 100 percent record in the PRO12 after winning their first four games of the season.
Gregor told glasgowwarriors.org: “We had to work hard to take the four points but the players are disappointed with their performance, especially in the last twenty minutes.
“They didn’t keep up the same accuracy and intensity that we’ve seen in previous games but all credit to Zebre for scoring two very good tries.
“When we ran at pace and used the ball well we looked dangerous.
"We scored three very good tries. The whole front row was involved in Dougie Hall’s try and the third was really good play between Sean Maitland and Byron McGuigan.”
Zebre came back into the game with two late tries and Gregor says he wants to use that period to identify areas they can improve.
He added: “It’s often good to have a situation like that so we can address the feelings the players had during that time and as coaches what we could have done better during that period. We’re always looking to learn and improve.
“We need to get the fundamentals right such as coming up in defence, being disciplined and taking the initiative.
“We’ve got good depth in the squad and there is real competition. It’s important that the players keep putting their hands up for selection.
“We’ve now used 34 players in our first four games and we’ve got four wins. Last year we used 51 players and you need that depth to compete throughout the season.
“The focus now is to improve from last night ahead of a very difficult game against Scarlets next weekend.”