A tactical contest appeared to be meandering towards a goalless draw until dozy defending allowed former Manchester City youngster Denis Suarez to evade the Liverpool backline and square to Adrian Lopez who tapped into an empty net.
The goal emanated from left-back Alberto Moreno being caught upfield, allowing space in behind centre-half Kolo Toure, although Klopp believes Liverpool are still very handily placed to reach their first European final since their Champions League tussle with AC Milan in 2007.
“I am not too happy with the goal we conceded. Counter-attacking in the 92nd minute makes not too much sense,” said Klopp.
“There is no explanation for this. If we had enough players in and around the box for protection it would be no problem but this situation is not allowed. “They played one chipped ball over Kolo [Toure], I don’t know where Alberto [Moreno] was, it was all confused and it makes no sense.
“But it’s only the first leg. It’s 1-0 and they have to come to Anfield and they know how strong we are. To be honest, I thought we would have more problems here but we defended really good and had our moments.
“It’s no problem. We now know more and this race is not over.”
Liverpool were first to threaten in the fifth minute as midfielder James Milner provided the ammunition from the right flank, only for Joe Allen to fire tamely into the grateful clutches of Villarreal goalkeeper Sergio Asenjo from 12 yards.
In a brisk opening, former Valencia striker Roberto Soldado, whose goal-shy stint at Tottenham was brought to an end last summer, fired across goal after a clever Bruno Soriano free-kick.
Villarreal, currently fourth in La Liga, cranked up the pressure midway through the opening period as Liverpool stopper Simon Mignolet repelled a Tomas Pina effort.
The two sides had kept 42 clean sheets between them this season so it was hardly surprising the first half ended goalless, although Villarreal top scorer Cedric Bakambu struck the outside of Mignolet’s post with a powerful header moments after the re-start.
Liverpool were next to rattle the woodwork as Roberto Firmino’s low drive was palmed onto the post by Asenjo, while the Reds were indebted to a superb one-handed Mignolet save to thwart Bakambu late on.
But with time running out and the stalemate looking a certainty, Suarez exploited space in behind the Liverpool defence and squared unselfishly for Lopez to calmly slot home – the Reds’ first Europa League defeat in 13 matches this term.