Head of rugby Nigel Davies selected a strong side for Sunday’s trip to central France as they looked to go one better than their last eight place back in 2010.
But Owens and co failed to find their form at the Stadium Amedee-Domenech and the Wales squad member insists the region are no longer happy with simply competing on the big stage.
“Maybe it is another learning experience but we’ve been learning and stepping forward for three or four years now and it’s getting frustrating,” said Owens.
“It’s time that we started coming to places like Brive in big games, in knockout rugby, and winning.
“We lost in the semi-final of the LV= Cup up in Northampton and didn’t learn our lessons from that and it’s happened again in the Amlin.
“We’ve just got to look forward to the league now and hopefully push for a top-four finish in the Rabo.”
Owens, who came on as a second-half replacement for skipper Matthew Rees, highlighted a lack of accuracy around the breakdown as one of the most disappointing aspects of the Scarlets’ performance.
The visitors were unable to put their opponents under sustained pressure despite having plenty of possession and Owens admits they made it hard for themselves against a Brive team who had won all six of their Amlin Challenge Cup pool games.
“Brive dominated the contact area and that’s where we probably lost it,” added Owens.
“We conceded too many turnovers. When we had the ball in the first half, I think we turned it over 70 per cent of the time and you’re not going to come to places like Brive and win if you do that.
“We knew how hard it was going to be coming to Brive but we did have confidence in ourselves. I don’t think we executed our game plan, though.
“We were under pressure at scrum time and we found it difficult. When we got momentum, we were fine but we were missing that little bit extra that we needed.
“I think the boys showed plenty of heart and plenty of spirit to stay in there right until the end but it’s a massive disappointment.”
