And Connacht bore the brunt of Ulster's frustration on Friday evening as Anscombe's men ran in eight tries in a thumping 58-12 victory.
Winger Andrew Trimble helped himself to a hat-trick while Paul Marshall (2), Tommy Bowe, Luke Marshall and Craig Gilroy all got in on the act.
Connacht scored two tries of their own through Dave McSharry and Darragh Leader, but they simply had no answer for Ulster's dominance - and Anscombe insists his side are only just getting started.
"You watch these games and you look at who you want to win," he said. "Am I happy that Ospreys beat Leinster? I don't know; it allows us to catch Leinster but it keeps Ospreys in the picture.
"At the end of the day, if we're honest to ourselves, and we'd be lying if we said differently, we'd like to have a home semi-final. But to do that we at least have to win two out of our last three.
"Munster have got Glasgow and if that goes Glasgow's way we're (still) second. And then we've got Leinster and if we win that we're first.
"So it is achievable and that's what we've got to do. A lot of people said (after Ulster's European Cup exit), 'What's to go for now?' Well, the season started in September and it was our goal to be successful in this competition.
"As a group, we're not going to be together ever again in four or five weeks time, so let's get back up. We've talked, we believe we're good enough, so let's show we are and get something from it.
"That was a pretty good response out there. Now we've got to rest up, look at our injury total and hopefully bounce back against Glasgow next week.
"It doesn't get any tougher, does it? It's like playing a European Cup quarter-final for the next five weeks - that's what we've got."
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