Substitute Adrian Lopez capitalised on a momentary lapse in concentration in the second minute of added time to give the home side the advantage ahead of the return in a week’s time.
On Liverpool’s last European appearance at home they staged a dramatic comeback to beat the then-favourites Borussia Dortmund and although the late drama went against them in Spain, Klopp remains confident.
However, he cautioned against another similar performance like the one against the German club.
“I am pleased with the performance, a lot of parts we did really good. Villarreal are a good side but Liverpool are a good side too,” he said.
“After controlling a game like this in most parts of the game a 92nd-minute counter-attack it sounds like it is – not too good and everyone knows it and it should not happen.
“I’ve seen some unbelievable mistakes but I don’t think about things like this. It happens.
“It was not too smart. There are lot of things we could ask but it makes no sense.
“It is not a moment for disappointment. If the players want to be angry for 10 minutes then do it and move on.
“To be honest it is the first leg. My first thought was ‘Sorry, but it is not over, you have to come to Anfield too and we will be ready’.
“With the help of Anfield we can do it – but please don’t compare with Dortmund.”
Midfielder Joe Allen had Liverpool’s best chance in just the fifth minute but when left-back Alberto Moreno, who rifled a late shot into the side-netting with substitute Jordon Ibe better placed in the middle, got caught upfield it left Kolo Toure exposed to the much younger Denis Suarez who squared for Lopez.
“We had this great moment with Alberto and a header from Christian (Benteke). Maybe the youth (inexperience) came through. Until then it was really a professional performance,” added the German.
“Things are possible with 1-0, it is not the biggest result in the world. Villarreal know a lot more about us and they will respect us.
“Now we have to find solutions to a few things but I saw we are in a good way. I saw a lot of things that show we can.” Villarreal manager Marcelino felt his side deserved the win, despite it being an evenly-balanced and often mundane game.
“Until the final whistle you can score or concede a goal and this time we were lucky enough to score in the very last minute.
“We managed a good result but we don’t know if it will be short or not until the end of the tie. “It was not an unfair result and we didn’t beat Liverpool by being lucky.”