Ulster led 9-0 following three Paddy Jackson penalties but that was as good as it got as their hosts came roaring back with Sean Maitland, Tommy Seymour and Mark Bennett all grabbing tries.
The result leaves Ulster third in the RaboDirect PRO12 table, with Glasgow Warriors one place and one point behind them with a game in hand, and fifth-placed Ospreys five points back.
Ulster have two tough clashes remaining as they take on Leinster on May 2 before finishing things off against Munster a week later, but Muller isn't about to accept any excuses in their hunt for the RaboDirect PRO12 title.
"Chatting to the Glasgow team after the match, they said that it was their biggest test of the season and they were obviously over the moon with the result. However, I think the scoreline didn't tell the whole story of the game," said Muller.
"I actually thought that in the first half of the match we played some good rugby. We built some nice phases but we gave away a try just before half-time that was completely against the run of play.
"In the second half we had some good periods, but to play with 14 guys for 30 minutes killed us. We had a try which wasn't allowed, they had a try which was allowed and that was a 14-point swing which was the difference between winning and losing.
"We have got a bit of a break now. We have got a week and we have to recover mentally and physically.
"We are playing two finals now because basically if we lose one of them there won't be any play-off chances. The pressure is on and we have to react."
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Guinness PRO12 Ulster News
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