Tries from Peter Murchie, Tommy Seymour, Tim Swinson and Nikola Matawalu extended Glasgow's winning streak to six games and made amends for their 18-10 defeat in Belfast last year.
But despite inflicting only the third league defeat of the season on the Ulstermen, Glasgow skipper Wilson insisted his side were not happy with the manner of the victory.
However, he admitted that recent results had given Warriors the confidence to look beyond a top four finish this season - and target the RaboDirect PRO12 title itself.
"It was a very important win for us. We have gone from wanting to be a top-four team, to being in the top two, and now after this we are going to push for the top spot," he said.
"We didn't put Ulster away as we have done with other teams but we should have done. We were angry that we did not turn the pressure we had into points, and that is a measure of how far this club has come to be in this position."
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