Left-back Alberto Moreno was culpable for Adrian Lopez's injury-time winner as he was caught napping up-field when Denis Suarez was picked out on a crafty run before the midfielder squared for Adrian Lopez to simply slot home into an open goal.
Klopp was of the belief that his Reds were good value for at least a draw in a match where they created some decent chances but conceded that their determination to get forward and produce a vital away goal contributed to their first leg downfall.
"Of course I'm not too happy with the goal we conceded in the last second," said the German.
"Counter-attacking in the 92nd minute makes not much sense.
"If we had enough players in around the box it was no problem but they played this one chip ball over Kolo (Toure), I don't know where Alberto was in this moment but that was the only big mistake we made in this game and they scored with it.
"That sounds like it is – not too good. Everyone knows it and it should not happen. Until then it was a really professional performance."
Liverpool will host the Spaniards in the return bout at Anfield next Thursday.
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