However, they failed to reproduce that display in the return fixture and defeat saw Ulster surrender top spot in the pool.
This time Anscombe is expecting nothing short of a repeat performance of Saturday night's 48-0 win at Ravenhill when they visit Italy on Saturday.
"We were sitting over in England this time last year and we were pretty happy with what we'd just achieved," he said.
"We didn't back it up - we let ourselves down and that took away the opportunity of a home quarter.
"Hopefully that's what life is all about - you learn from your mistakes and your hiccups. Hopefully we have learned from ours.
"We've got enough experience and we know that no two days are the same in this game. We know it's another challenge, a different challenge, next week."
However, Anscombe is well aware of the different challenge Treviso, whose head coach Franco Smith will step down after the match, are capable of presenting on Italian turf.
Despite sitting third from bottom in the RaboDirect PRO12, Smith's side have already beaten Munster and Connacht at home, as well as holding Cardiff Blues to a draw.
"We're not at home - it's in Treviso and they have a proud home record," added Anscombe. "Just look at their performances there this year.
"When you're playing teams that have that quality and the number of internationals they have, they're not going to back up next week with another performance like that, so we're not going to kid ourselves that it's going to be a walk-over.
"There were things there that were good today, there were things that we have to be better at, and they'll bring a different challenge next week."
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