Liverpool will face holders Sevilla in Basel on May 18 after a Bruno Soriano own goal and efforts from Daniel Sturridge and Adam Lallana at Anfield on Thursday secured a resounding 3-0 win and a 3-1 aggregate success.
The Reds had made an inauspicious start to their Europa League campaign when Klopp succeeded Brendan Rodgers last October, but having now eliminated Augsburg, Manchester United, Borussia Dortmund and Villarreal, they will play in their first European final since 2007.
"To go to a final you need a little a bit of luck in decisive moments, but most of the time you need outstanding performances," he told his post-match media conference.
"When I came here, the tournament didn't sound too nice for people. Three draws (actually two). It was a difficult group.
Sturridge sends Liverpool into Europa League final
"We came through with a nice game in Russia (beating Rubin Kazan 1-0). That was good.
"We felt really comfortable in this tournament. We liked going to different countries and adapting to different circumstances, different temperatures. I like this in football.
"The problem we had was around these games (there were) so many other games, so we couldn't really be focused on this.
"In 2016, the team showed a lot of times what they're capable of and what they could be capable of in the future.
"That's a really good sign. That's more important for me as a manager, but then, when you perform in the right moments, like we did tonight or against Dortmund or against United or Augsburg, you want to have (it) all.
"That's what we try now (in the final). Now we are there and it's a great opportunity and we will take it."
Villarreal had procured a stoppage-time lead in last week's first leg through substitute Adrian Lopez's strike, but their advantage lasted less than seven minutes of the return fixture at a raucous Anfield as Bruno turned Roberto Firmino's cross into his own net.
Sturridge, sliding in, had put the Villarreal captain under pressure and he would go on to put Liverpool ahead in the 63rd minute, finishing coolly from Firmino's scuffed volley, before setting up Lallana's third.
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Klopp had left Sturridge on the bench for Liverpool's three previous games in the tournament and he praised the injury-prone England international for seizing his opportunity against Villarreal.
"Great game, great game," said the German, who has already seen his side go down on penalties to Manchester City in this season's League Cup final.
"You'll see now, when Daniel Sturridge is fit he's an unbelievable, unbelievable striker. Everybody knows this.
"But even he needs players to play with. I knew about his quality before I came here. Now I know it better. Great player. Good to have him here."
Meanwhile, former Liverpool striker Luis Suarez also congratulated his former club for making it into the finals.
He wrote: "Congratulations to all at LFC for moving to the final!! Congratulations friends!!"
Felicitaciones a todo el @LFC por pasar a la final!! Enhorabuena amigos!! #MartinSkrtel @Phil_Coutinho!
— Luis Suárez (@LuisSuarez9) May 5, 2016
Villarreal coach Marcelino, whose side secured a Champions League play-off place at the weekend, admitted that Liverpool had been superior and lauded their "huge" intensity.
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But he criticised Hungarian referee Viktor Kassai for his handling of a niggly game, in particular the decision to dismiss centre-back Victor Ruiz after two yellow cards in either half.
"We tried hard after the opening goal, but it was tough against an opponent who played with a huge amount of intensity," he said.
"It was on the margins of the rules at times, but it was allowed. By the sending off it was game over.
"You saw what happened. When the referee was letting so much go, to see a player sent off for those two incidents, you make your own opinions."
The disappointed Marcelino suggested that Klopp had celebrated Liverpool's goals with more zealousness than he would have, which drew a stinging rebuke from the Liverpool manager.
"I would not be like him one second in my life," Klopp said. "And he's a great manager."
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