The reigning Aviva Premiership champions will secure a Heineken Cup quarter-final place if they claim just a point against Italian hosts Treviso on Sunday.
Victory in the Pool Five encounter, though, should secure a home tie and enhance Saracens' prospects of reaching the Twickenham final in May.
"We were disappointed last year about being knocked out so early," Saracens centre Barritt said.
"We will take it step by step, but it's a massive ambition for the club to be up there with the Munsters and Toulouses of this world.
"Beating Biarritz last week was a massively-important win. We spoke during the week about it being almost a final.
"Biarritz and us were really the two teams that could progress from the pool, so we really pulled out the stops and got a crucial win.
"We've got a lot of resolve in the team that has built up over two-and-a-half seasons. The guys know how to pull themselves out of tough situations.
"We've still got another big game in Treviso this weekend. They've pulled some major scalps this year, so it is definitely not going to be easy.
"They beat Biarritz down there in the Heineken Cup, and they have done well in their league. They are a well-coached side with talented players across the field, and on their day they can beat anyone."
Barritt lines up in a Saracens side that also contains his England squad colleagues David Strettle, Owen Farrell, Charlie Hodgson, Matt Stevens and Mouritz Botha, while Biarritz and the Ospreys - who meet at Stade Aguilera tomorrow - are playing for the runners-up spot.
Pool Two will also be decided on Sunday when Cardiff Blues and Edinburgh, who are tied on 17 points, host Racing Metro and London Irish, respectively.
A bonus point success for the Blues in Wales would guarantee they finish top, but Edinburgh could still qualify, either as a group winner or one of two best runners-up.
The Blues will again be without injured Wales centre Jamie Roberts just a fortnight before the RBS 6 Nations kicks off, while Gavin Henson is replaced in midfield by Gavin Evans.
"Our first thoughts are to keep our focus and a winning mentality," Blues backs coach Gareth Baber said. "We need to get the win, and then see where we are at the end of it.
"It's no good talking about winning bonus points. It is easy to say what you are going to do before the game, but things change during the match.
"However, we are fortunate to have the quality players within this group that are able to adapt to the situation in a game and make it count."
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