Director of Rugby Les Kiss believes back-to-back wins over Harlequins have given Ulster hope of reaching the European Champions Cup quarter-finals.
The Irish province, who beat Quins 52-24 in Belfast on Friday, have failed to progress for the last three seasons.
They are currently second in Pool One behind favourites La Rochelle who have a maximum 15 points from three games.
“We have a chance to do something here, but La Rochelle are the form team in Europe,” said Kiss.
Stuart McCloskey, Craig Gilroy, Charles Piutau, Alan O’Connor, Andrew Trimble and John Cooney all scored tries for Ulster in the big win at the Kingspan Stadium.
Scrum-half John Cooney landed five conversions and four penalties for a 27-point haul.
The victory puts Ulster in a position to potentially qualify with two rounds remaining though, even at this stage, their best chance may be as one of the three best pool runners-up.
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“We were anxious to get out there and finish the deal,” added Kiss.
“And the boys wanted to make a major statement in this game in front of the fans.
“It certainly was a spectacle that is for sure.”
Ulster only led 16-12 at half-time before pushing on late in the game and Kiss admitted he was frustrated at some of their defensive lapses.
“It was a bit too loose at times but it was good to get 52 points,” he said.
“The key focus for us was to concentrate on the basics of the game.
“I think we had just got a bit away from that and I thought we were a little bit lateral at times.”