Goalkeeper, David de Gea missed the last spot-kick to hand the Spanish team their first major trophy.
Gerard Moreno put the unfancied Spaniards ahead in the 29th minute to stay ahead at half time.
However, Edinson Cavani levelled early in the second half.
Both teams failed to get the winner throughout the rest of the normal time and extra time.
In an entertaining penalty shootout, all 20 outfield players converted their penalties and Villarreal goalkeeper Geronimo Rulli also scored from the spot.
With this victory, 5 Spanish teams will play in the UEFA Champions League next season.