However, full focus is now on the next batch of RaboDirect PRO12 games, with the Ulstermen looking to tighten their grip on a top-four spot.
And Anscombe has targeted the next four clashes - starting against Ospreys on February 7 - as his side look to replicate their European form.
"We always believed we were contenders," Anscombe told the Irish Times.
"Yes, we went through unbeaten which is something to be proud of but also to go to places like Montpellier and Leicester and have away wins is very satisfying.
"When we get back to this, in two months time, we've put ourselves in a position that we can confidently have a crack at it. But we'll worry about all that later.
"Now, though, we've got four pretty important Rabo games and three of them are at home so we have to make sure we keep getting results.
"I think the next four games will be crucial to us to show how we've grown squad depth.
"We know we're in contention in one competition and we know we've got to be in contention in the other one as well."
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