That defeat dropped them to eighth in the table as they now sit three points behind Connacht, who currently hold the sixth and final automatic European qualification spot.
The West Wales region have a golden opportunity to bounce back when they travel to Stadio Sergio Lanfranchi to take on bottom-of-the-table Zebre this Saturday and Owens is hopeful his troops' frustrating display against Edinburgh will benefit them in the long-run.
"We are all disappointed with the result against Edinburgh which has put us under more pressure," said Owens.
"But perhaps it was the eye-opener we needed to put things right and we have an opportunity against Zebre to do that.
"It is disappointing and frustrating that we are relying on other results, but if we get a win on Saturday and win our three remaining fixtures after that we are hopeful we can finish in the top six.
"Not making Europe would be a major blow but a thing we haven't spoken about. We are looking at staying positive and looking at that top six.
"This region's history and tradition in Europe is huge and as a squad you want to be playing against the best players in Europe and that is motivation enough."
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