On the night, Stuart Hogg's solo try wasn't enough to seal victory, but the Glasgow head coach is pleased with the way his men fought their way back into the game.
Speaking to glasgowwarriors.org, he said: "I think we improved as the game went on and it is great to see the character of the players that they were trying to find a way to win and almost did. It was the response we wanted to see from the team.
"We were struggling to go through the phases in the first half but in the second we retained ball and won a lot of penalties off that which gave us opportunities to win the game.
"A game of rugby is a lot of things, it's about effort, it's about aggression and Munster came out with a lot of aggression around the contact area which forced errors.
"Munster are an excellent team and they're excellent when they are ahead as well due to their very good defence.
"They just had a little bit more than us on Saturday which is tough for us to take because obviously we need the win to stay in the mix".
Looking ahead to the final few games of the season Gregor is confident that his men can get back to winning ways and end the season on a high.
He said: "We have only got three league games remaining, two of them are at home and we certainly want to play as well as we can.
"For a number of players the Zebre game might be their last at Scotstoun so we want to play these last few games as if it is our last together and continue to work on improving.
"The things we did well against Munster we want to repeat, but things we didn't do as well we will work hard on at training and make sure we are better on Friday."