The heavy loss at La Ceramica meant Atletico missed the chance to finish third in La Liga, while Villarreal secured a top-three finish for the first time since the 2007/08 campaign. It was also only the second time during Diego Simeone's reign that Atletico had conceded five goals in a league match.
Koke admitted the campaign had fallen well below expectations despite positive runs in the cup competitions.
"It leaves a bitter taste in my mouth," the midfielder said after the match.
"In the Champions League it was exciting, in the Cup we lost on penalties, but in the league we've been a disaster because we were not able to fight for the title. We need to be higher in the table and use this as motivation for next season."
Atletico finished 25 points behind champions FC Barcelona and ended outside the top three for the second time in three seasons under Simeone.
The visitors were overwhelmed by a sharp Villarreal side inspired by departing coach Marcelino García Toral. Veteran midfielder Dani Parejo marked his final appearance for Villarreal by opening the scoring from the penalty spot after Nicolas Pepe went down inside the box.
Ayoze Perez doubled the lead minutes later with a clinical finish before Georges Mikautadze added a third from close range. Atletico briefly responded through Marc Pubill after a mistake from goalkeeper Arnau Tenas, but Pape Gueye restored Villarreal's three-goal cushion before half-time with a powerful strike.
Perez then completed his brace early in the second half after another dangerous move involving Nicolas Pepe, as Villarreal comfortably closed out the match in front of their home supporters.
Despite the disappointing league finish, Simeone insisted he still viewed the season positively.
"We had a season somewhere between good and very good," Simeone said.
"We reached the Champions League semi-finals and the Copa del Rey final while playing 61 matches. Villarreal had a very good season too, but they only had one competition to focus on. We gave our fans many important moments, even if everybody always wants to win the league."
Atletico are now expected to enter another busy upcoming transfer window, with fresh backing from Apollo Sports Capital set to strengthen the club ahead of next season.
Osasuna have decided to part ways with head coach Alessio Lisci after just one season in charge at El Sadar, following a dramatic end to their La Liga campaign that saw the club dragged into a relegation fight.
Chicago Fire manager Gregg Berhalter has confirmed that the MLS club are in talks to sign former FC Barcelona striker Robert Lewandowski after the forward decided to leave the Spanish champions.
Real Madrid are preparing for another emotional farewell at the end of the season, with veteran defender David Alaba confirming he will leave the club when his contract expires in June.
Real Madrid coach Alvaro Arbeloa has confirmed he would leave the club after Saturday's final La Liga match against Athletic Club, admitting he often put the club's interests ahead of his own during a difficult four-month spell in charge.
