The French giants suffered semi-final heartbreak at the hands of Leinster last April, but they have now nudged the defending champions towards elimination from this season's tournament.
Speaking after another pulsating clash, Cotter said: "We intend to go the whole way. It's a game of rugby - it doesn't always go the way we want, but our intention is to go as far as we can."
He went on: "Last year we lost a semi-final in Bordeaux. Goodness knows what would have happened if Wesley (Fofana) had scored that try (in the last minute of the semi-final against Leinster).
"We didn't get a crack at the final. We would like to get there and see if we can get over the line and take the title. That is our firm intention."
Successive defeats in this double header - Leinster were 15-12 losers in Clermont last Sunday - have the Irish province clinging onto their title.
Head coach Joe Schmidt admitted they need a miracle to make the knockout stages.
"Miracles happen in sport, I guess, but mathematical long shots very seldom come into being," admitted the New Zealander, whose side earned a losing bonus point thanks to a late Fergus McFadden try.
Schmidt pointed to the strength in depth at Clermont's disposal, adding: "I don't think we have the same depth as some of the big-spending French clubs. It's hard to take defeat two weeks in a row, with the amount of effort the players put in.
"The other challenge for champions is they always look pretty good when they are on top. It is how they come back from adversity that is the real challenge."
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