Edinburgh head coach Richard Cockerill praised his side's resilience against La Rochelle but accepted that the best team had come out on top in their Champions Cup opener.
Jules Plisson kicked an early penalty for the French outfit before Raymond Rhule crossed for a well-worked try to move the visitors into an 8-0 lead.
Jaco Van Der Walt got Edinburgh on the scoreboard with a penalty to cut the deficit to five points at the break.
But Edinburgh's resilient defence came undone two minutes into the second half when Henry Pyrgos miscued a high ball and Jeremy Sinzelle capitalised, carrying three defenders with him as he powered over the line.
The hosts hit back when Blair Kinghorn raced on to Chris Dean's clever grubber kick but Van Der Walt missed the conversion as Edinburgh fell to a hard-fought 13-8 loss at BT Murrayfield.
"It was tough, they're a good side and they put us under a lot of pressure," Cockerill said.
"We didn't control field position very well in that first half and we let them play on top of us a little bit, but we were in the game and we were there at the death trying to win it so credit to the players.
"It was tiny margins in that second half. We don't gather one high ball and it bounces the other way and you end up giving them points, which is the difference at the end.
"I'm not going to complain about the result. We could have done better, we could have been in there for a draw or even a win at the end, but we weren't quite good enough."
The defeat leaves Edinburgh facing an uphill battle to make it out of the pool stage and into the quarter-finals of this year's Champions Cup but Cockerill insisted that his team still has plenty to play for.
"We're a good side and we can compete at this level," he said. "We're not giving this away.
"We're going to pick our best team for next week and we're going to go to Sale and try and win. It's not all over tonight, we got a losing bonus point and there's still lots to play for.
"There's still this competition, there's still the Challenge Cup to drop in to."
