The Yellow Submarine, who finished fourth last season, seemed set to survive as they withstood a second-half onslaught from the Europa League winners.
However, Falcao's 88th-minute header from Diego's corner, allied to victories elsewhere for Rayo Vallecano and Real Zaragoza, meant it was Miguel Angel Lotina's side who join Sporting Gijon and Racing Santander in the bottom them.
The victory however was still not enough for Atletico to seal Champions League football as Malaga's 1-0 win over Sporting Gijon meant that Diego Simeone's side had to settle for fifth place.
In a game marked by tension rather than quality, it was the hosts who had the better of the opening period as Marco Ruben fired just off target from the edge of the area before Carlos Marchena's header whistled past the post minutes before the break.
After half-time though Atletico began to dominate and Villarreal were thankful to Diego Lopez as he made fine saves to deny Tiago and Eduardo Salvio, while Felipe Luis also saw an effort come back off the bar.
At the other end Thibaut Courtois got down well to turn away Marcos Senna's fiercely struck free-kick, but the nerves eventually got the better of Villarreal as they began to sit deeper and deeper in the final 10 minutes.
And that anxiety was punished as Falcao continued his and Atletico's excellent week as he rose above the defence to power home Diego's corner despite Lopez's best efforts.
Ruben had one final chance to save his side, but his header from Nilmar's cross in stoppage time slipped just wide to the frustration of a disconsolate El Madrigal crowd.