Neither team dominated the proceedings with not many chances getting created in the entire game.
Villarreal came close to breaking the deadlock at the start of the second half. However, Cedric Bakambu's header hit the post.
For Liverpool, Roberto Firmino created the best chance in the second-half but his strike hit the post following a deflection by the Villareal goalkeeper Sergio Asenjo.
Klopp wasn’t happy with his side conceding a late goal.
“A counter-attack in the 92nd minute doesn't make too much sense to be honest, but it's only the first leg. We had no luck today and they know how strong we are at Anfield,” he said.
Klopp would be hoping his side to recreate the quarterfinal magic at Anfield when they staged a remarkable comeback to beat Borussia Dortmund after being two goals down in the second half.
In the other semifinal, defending champions Sevilla drew 2-2 away at Shakhtar Donetsk.
The Spanish club took the lead in just the sixth minute through a strike by midfielder Vitolo. The home team however roared back to score two goals in the space of 12 minutes.
Just when it looked the Ukrainian side will take a one goal advantage to Sevilla in the second leg, the Spanish side scored a vital second away goal with just eight minutes left.
Kevin Gameiro converted the spot kick to give Sevilla an advantage.