Eighth-place Warriors are nine points adrift of the top four and a play-off place, but have a game in hand.
Townsend told BBC Scotland: "Nine games to go and there are a few tough ones.
"We play Dragons next. We've got to do a professional job, play well down there and keep the momentum going."
Bryce, who scored Glasgow's decisive fourth try in the 27-24 bonus-point win at Kilmarnock's Rugby Park in foul second-half conditions, said: "It's all about momentum in this league.
"We managed to show the Warrior spirit in the end and get the win. The boys are ecstatic. Hopefully we can kick on."
Munster recovered from two early tries by Glasgow prop Sila Puafisi to score two tries through a prop of their own, Dave Kilcoyne.
Glasgow's Duncan Weir and Mike Sherry for the visitors - while they were down to 14 men - traded tries, but it was Munster who led by two points before Bryce darted over in the corner to end a four-game winless run.
Townsend added: "I was concerned at half-time. We had started the game well but then Munster were outstanding.
"We played well when we had ball in hand. I thought we showed ambition and real pace in our game.
"Dragons next Thursday is a challenge for us because we won't see a number of our players at any training session because they will be with Scotland."
Glasgow number eight Josh Strauss was man of the match and may have shown enough to force his way into Vern Cotter's Scotland squad for the Six Nations match in Rome next Saturday.
"Josh was in really determined mood this week," said Townsend.
"By his own admission he had not got back to his best form coming off the bench in the last two games. He had been missing for the last four or five weeks.
"We thought he played really well before his concussion in the second Edinburgh game.
"He wanted to be captain this week. He had set a goal of a number of ball carries in the first half so you could tell he was up for it. When he plays like that he gives us real go-forward."
Glasgow Warriors coach Gregor Townsend and Glenn Bryce, the winning try-scorer in their Pro12 game against Munster, stressed the importance of building a head of steam to reach the play-offs.