Having won five of their six European pool fixtures Anscombe's troops might have been expecting to welcome the Premiership outfit to Ravenhill in April.
But Ulster coach Anscombe insists they are not daunted by the last-eight tie.
"We have to be confident and the fact is we haven't been beaten out of Ireland this year which is something we can be proud of," said Anscombe.
"We have travelled well and Saracens are comfortable away from home as well, they have a quality team with a lot of international players and they are a hard team to beat.
"We got through, we won our pool so there are more positives than negatives. It's the first time we topped our pool, first time we have won in France so maybe we'll leave a home quarter as a first for next year.
"The fact was we were in a tough competition and you just have to look at the standard and where all those teams are in their leagues.
"You could argue we had the toughest pool, Northampton are fifth in England they were beat by Glasgow who are second in the Pro12.
"It was a tough pool and we came out of it with five wins so it isn't all too bad. We can get over critical at times but five out of six doesn't happen too often.
"We are one of eight still in the competition and there are 16 teams not enjoying the thoughts of what a quarter-final brings to them."
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