DTH van der Merwe grabbed two first-half tries for the Scots with Chris Fusaro and Kevin Bryce also going over to give Warriors a 26-0 lead at half time.
Dion Berryman scored for Zebre just before the hour mark but there was no real sign of a comeback for the Italians and the Scottish side saw out their victory comfortably.
And although Townsend was relieved to see his side bounce back from their 22-10 defeat to Munster last week, he was disappointed with their second-half performance.
"When the weather came down, especially in the second half, there wasn't much rugby," he admitted.
"If you were a scrum connoisseur, you would have loved the last ten minutes of the game, but it was job done.
"We played quite well in the first half, clinical at times, obviously drew penalties and we got the tries that we were looking for tonight.
"We'll be concerned that we conceded a try. It was a goal in the second half to ensure we don't concede a try.
"We have to be better, we have to rise above it. The game, when the weather is poor, it does get confined to the forward exchanges and obviously we weren't disciplined enough in that area in the second half.
"I believe the squad we have now is stronger. We've got a tough run-in, tougher than we had last year.
"But we're set in a good position, we're sitting top of the league just now and we'll be either first or second when we play our next game against Leinster."
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