Liverpool loses 3-2 to Toulouse, West Ham and Marseille top of their groups
The stunning upset in France came courtesy of goals from Aron Donnum, Thijs Dallinga and Frank Magri as Liverpool sank to their first defeat in the Europa League this campaign.
However, the game was not without controversy with VAR intervening to rule out an equaliser deep in injury-time from Jarell Quansah.
"It was well deserved to lose because they won pretty much all the decisive challenges, battles," said Liverpool boss Jurgen Klopp as his side missed a chance to book their place in the knock-out stages.
Toulouse now sit on seven points, two behind the Premier League club and three ahead of third-placed St Gilloise in Group E.
With 36 minutes gone, Donnum pounced on Kostas Tsimikas and robbed him of possession before slotting home via a deflection to give Toulouse the lead at the break.
The buoyant hosts got a second when Dallinga took a touch in the box and drilled past Caoimhin Kelleher on 58 minutes.
An own goal from Cristian Casseres on 73 minutes gave Liverpool a lifeline but the hosts, pushed on by a vibrant home crowd, punched back immediately.
Three minutes later, Kelleher could not hold a firmly hit cross and Magri was on hand to restore Toulouse's two-goal buffer.
Diogo Jota, on for Diaz, struck a second for Liverpool in the 89th minute.
The hosts were able to see the game out to claim a precious three points, but not before an equaliser seven minutes into injury-time by Quansah was ruled out after video review for an adjudged handball much earlier in the build-up.
Last year's Europa Conference League winners West Ham ground down Olympiakos with a Lucas Paqueta goal on 73 minutes being the difference between the two sides.
"I'm really pleased that we got the result. We didn't play as well as we'd have liked