Harlequins led 7-6 at the break but the second-half introduction of Nikola Matawalu and DTH van der Merwe sparked the Warriors into life with Niko grabbing two tries and DTH rounding off a powerful display with length of the field run.
But a couple of late defensive lapses saw Quins edge ahead to take the win
The Glasgow head coach told the Evening Times: "You want to win, but in general I was very pleased with what I got from the boys.
"When you look at a Harlequins side that started with seven full England internationals in it, compared to the side we started with, plus this was their third and final build-up game and just our first, we can be very happy with the way things went.
"I thought we had some great contributions from our new players. Alex Allan had a fantastic game and Euan Murray carried ball well and put some great tackles in.
"After the break DTH and Niko came in and got in on the tries and I thought we offered a lot more intent. DTH has got himself into great shape.
"Defensively we can and will be better but this has given us a great foundation to build on and we can now look forward to the trip to London Scottish with some optimism.
"But you look at the quality of the catch-passing, the lines we ran and penetration we had and there was an awful lot to be happy with."