With more than 20 players unavailable due to Scotland duty or injury, the Warriors fielded a makeshift line-up in Cork with a number of players who have had limited game time up to now.
Speaking to BBC Scotland, Connor said: "These fringe players, myself included, shouldn't be worried about screwing up or letting the team down.
"They should ask: 'what can I do to get out of the fringe player label?'"
Connor, who can play at stand-off, centre or full-back, started the season as a full member of Gregor Townsend's squad, but moved to London Scottish on loan in October.
The English Championship side secured the Canadian's services on a permanent basis two months later, with the proviso that he could return to Glasgow to cover absences brought about by the Six Nations.
With Finn Russell and Peter Horne on international duty, and Duncan Weir out of action with a bicep injury, Connor will remain on loan at Scotstoun until the end of the season.
"It was good," he said of his spell with London Scottish. "Playing 80 minutes every week is quite nice, better than sitting around up here not playing.
"It prepped me and gave me some good game fitness to come back up here and play.
"The Munster game was a whole other level of pace compared to the Championship.
"All the boys are feeling it; they're burning the lungs a bit because it was a pretty quick game. It's tough to match the PRO12 speed with Championship rugby.
"I felt a bit of pressure - a top-of-the-table clash, playing 10 and being told to run a game-plan and kick my goals. But at the same time, I thought: 'you can either sit here and be nervous and be worried about screwing up, or you can be excited about excelling'.
"Even if you make a mistake, at 10, the nice thing is you have the opportunity to rectify it almost immediately."
Connor, who is keen to prolong his stay in Scotland beyond this campaign, is gearing up for another test as Zebre visit Scotstoun on Friday.
He was a replacement last month as Glasgow trounced the Italians 54-10 in Parma, with the hosts entangled in internal turmoil that resulted in the resignation of head coach, Andrea Cavinato and director Roberto Manghi.
Zebre have shown improvements in the intervening period in defeats to Leinster and Connacht, and Connor expects a far sterner challenge in the return fixture.
"When we played them three weeks ago, they weren't really up for it," he acknowledged.
"They weren't mentally there. They were making mistakes that they probably normally wouldn't make. We caught them when we were at a very strong point and they were at a very, very weak point.
"The last two weeks they've played they've really stepped up. It'll be a different Zebre team to what we played in Zebre. It's a huge game for us coming off a loss and coming back home."