Two weeks on from crushing the Coupe de France winners 5-1 at Anfield, Liverpool had the chance to confirm a spot in the last 16 with a fourth continental win on the trot at Stadium Municipal.
The Reds entered the clash boasting five-point leads over Toulouse and Union SG, whose defeat to LASK Linz meant that Liverpool would have been guaranteed to finish first with two games to spare had they triumphed.
However, a second-string side fell behind in the first half as Aron Donnum robbed Kostas Tsimikas of the ball before firing home a deflected strike, and Thijs Dallinga's fine finish across goal doubled the hosts' advantage early in the second half.
An unfortunate Cristian Casseres Jr own goal halved the deficit, but Toulouse restored their two-goal cushion just three minutes later, as Frank Magri slotted home after Caoimhin Kelleher palmed Gabriel Suazo's cross into his path.
Diogo Jota's fine solo strike off the bench gave Liverpool a shred of hope heading into a seven-minute injury time period, where Jarell Quansah lashed home what he and the travelling crowd believed was a last-gasp equalising goal.
However, play was brought back for an Alexis Mac Allister handball, as the Argentine controlled the ball with his chest before it struck his arm, and after some confusion, the Reds' leveller was ultimately disallowed.
As a result, Liverpool missed the chance to wrap up last-16 qualification early, although Klopp thinks that Mac Allister and his side could feel hard done by, telling reporters: "I only saw the video back now and for me it's not a handball, but how can I decide that?
"The ball goes to the chest and then I don't see a contact with the arm, to be honest. Maybe they had a different picture than I had. It was pretty long ago before we scored the goal and I thought, 'Where is the free-kick?' I didn't see it properly but I heard there could have been a penalty for us in another situation, I don't know.
"Actually, I am a bit more concerned about [the fact that] I would have loved us to have played better, to be honest. That's my main issue tonight. In a football way more aggressive."
Liverpool remain at the summit of Group E and will guarantee a top-two finish by overcoming LASK Linz at Anfield in three weeks time, but Toulouse have now cut the gap down to just two points.
Klopp's side are now winless in two fixtures after a lacklustre performance in a 1-1 draw at Luton Town, but the German admitted that his side deserved nothing at Stadium Municipal, adding: "It was well deserved to lose because they won pretty much all the decisive challenges, battles. We have too many situations where we should have won the ball but we didn't.
"In the end, we were intense - we threw everything in, but the problem is in a football game you have to make the decisive things in the right moment to do them right. We cannot concede the goals we conceded again.
"Yes, the result is the opposite of good, but the performance was just not good enough. I am not concerned, I just see we have to change and we will, definitely."
The Reds will now endeavour to bounce back and enter the international break on a high when they host Brentford in Sunday's Premier League showdown.