But a resurgent Glasgow piled on six more tries after the break - including a double for man-of-the-match Peter Horne - to leapfrog Scarlets into third with a 43-14 victory.
The reigning champions have now won seven PRO12 games on the trot, though Townsend says the result does not reflect the type of challenge they were given in Italy.
"We're delighted to come away with the win and to get more than four tries certainly helps our position in the table," he said.
"It was one of those games that you'll probably look back at in a year or two and just see the score and think that was a bit of a one-sided game, but a lot happened during the game and before it.
"We had up to 15 of our squad down with illness on Monday and Tuesday including me, so when we were thinking about how the week was going to pan out on Tuesday morning it wasn't looking great.
"But I have to say the players put huge effort in and we trained an extra day because we didn't have a big enough squad to train on Tuesday and for them to play so well in the second-half shows their character and resilience."
Glasgow have timed their winning run to perfection as with just three games to go, they now have a six-point buffer inside the top four over fifth-place Ulster.
Townsend added: "It's an exciting time of the season and there are a lot of teams still in the race for the play-offs.
"We've done really well over the last few weeks and we've got to keep this momentum going. We want to secure a place in the play-offs and do all we can to get a home semi-final."
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