The win left the Warriors just a single point behind third-placed Ulster, but a bonus-point victory over Scottish rivals Edinburgh - their game in hand - will see Glasgow move into second spot at the expense of Munster.
And Townsend admits with so much to play for at the business end of the season, his players can ill afford to take their eye of the ball with Edinburgh now in their crosshairs.
"The Ulster victory was massive, but what we can't do is have any falling off," he told the Glasgow Evening Times. "Edinburgh is now the biggest game of the season for us and we have to make sure everything in our preparation is perfect for it.
"But we have put ourselves in a very strong position to try and claim second place and the home play-off semi-final that goes with it, given we are now just four points behind Munster, with a game in hand and two of our last three fixtures at Scotstoun.
"The other plus for us is that Munster and Ulster will play each other at Thomond Park on the last Saturday of the season and something must give there.
"But none of that is any good if we don't beat Edinburgh. So it's maybe a cliché, but the next game is the only game we are interested in."
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