Despite having a number of fresh faces in the team, Ulster completed a first season's double over Irish rivals Munster thanks to a hard fought 19-17 win at Thomond Park.
Fly-half James McKinney starred with the boot, kicking 14 points, while Michael Heaney also dotted down for his first Ulster try.
And while thoughts undoubtedly turn quickly to their away clash with reigning champions Leinster, Anscombe believes it is important for his side to savour their success.
"It was a bit tough there at the end there but credit to the guys, I thought they were outstanding for 80 minutes," he said.
"The tackles they got through today was outstanding, a lot of them have not had a lot of game time, we asked them to take this opportunity and to a man they did that.
"It's a credit to the boys, in real difficult conditions, against a strong Munster team and for this young side to come and play like this, hats off to them.
"You have to enjoy these special days. We'll enjoy this and then focus on Leinster after that."
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