The result was all the more pleasing for Muller whose side have struggled against Glasgow in recent seasons, despite beating them on the opening day of last campaign as well.
But the South African lock has warned his side not rest on their laurels ahead of a trip to the reigning RaboDirect PRO12 champions.
"It was a good start, we obviously haven't had great results against Glasgow in the past," Muller told the Ulster website.
"To get a win over them and deny them a bonus point was a good effort from everybody.
"It was still far from perfect though. There were a lot of mistakes and a lot of things that we need to work on, but it was a good start and hopefully we can continue that.
"We've really trained hard in pre-season to get everything ready for the start of the season and it's been good fun."
While Anscombe's men kicked off their campaign on a winning note it was less good news for defending champions Ospreys who came unstuck in Italy against Treviso.
And Muller has warned his side to expect a backlash when they travel to the Liberty Stadium on Saturday.
"They lost against Treviso at the weekend so obviously they're going to come out on fire, and really want to prove a point," he added.
"We haven't had great results, especially against Ospreys and also in Wales - I don't think we won one game in Wales last year.
"They're a good side, they're really physical up front and they've got a lot of internationals in that back of forwards.
"Obviously they're massive favourites for it but anything can happen, and we're excited to go down there and get a result."
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