The boot of fly-half Paddy Jackson had fired Ulster into a narrow 6-3 half-time lead, and as the rain subsided after the break it was the visitors who seized control as flanker Chris Henry crossed on the hour mark.
Jackson left Scotstoun Stadium with a personal haul of 14 points to secure the win and Anscombe insists it was a victory which demonstrated why his side have been so difficult to beat this season.
"We showed a lot of character out there, the boys battled their way through tough conditions against a very good team," he said.
"It's not easy to come here and get a victory as other teams I'm sure will find out.
"You have got to be able to work through things because the game of rugby doesn't always go the way you want it.
"If you don't have that character and attitude to hang in there and battle through the tough times, you won't come out the right end.
"We have done that a few times this year, and shown there is a bit of character there. That's a good benchmark to build a good team from."
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