Bruno Soriano put through his own net early on, before Daniel Sturridge and Adam Lallana scored the goals which set up a final clash against Sevilla in Basel later this month.
The Reds were in imperious form, never allowing the visitors to settle and add to their goal advantage from the first-leg, and Klopp had nothing but praise for the performance his team put in to down the La Liga side.
Speaking to BT Sport 1 after the game, the German head coach said: “Wonderful. A brilliant game from my side.
“What power, what a performance. Attitude, readiness, everything. The first 30 minutes was emotion and the last 15 minutes.
“The whole night. What can I say, it was unbelievable.”
Liverpool came out of the traps in incendiary fashion, the players seemingly fired up after a rousing chorus of ‘You’ll Never Walk Alone’ from the Reds’ faithful, who were gathered together at Anfield for the first game since the Hillsborough inquest verdict, which concluded the 96 Liverpool fans who died at the stadium in 1989 were unlawfully killed.
The atmosphere was reminiscent of the famous European nights which have gone down in history on Merseyside, and Klopp knows that winning every game would be easier if the atmosphere was always replicating what was seen against Villarreal.
He added: “If this is the difference from the Premier League then it’s easy to change – create atmospheres like this in every game. We know what we have to do Sunday.”