They can follow it up with a win at home to Elche on Sunday.
The club's hopes of qualifying for Europe had begun to wobble with their poor form, but the three points won in Madrid keep Marcelino's men eight points abreast of Espanyol, while they are just two points behind fifth placed Sevilla.
Asenjo emphasised the importance of the win at Getafe to the team's morale as well as their ambitions for the remainder of the season, and stressed it would give his team further confidence against Elche.
"Getting those three points gives us the opportunity to string together six points consecutively, which is fundamental if we want to finish the season in the European spots," he said.
"To do that we need to stay concentrated, recover from our exertions against Getafe and go all out to win at home on Sunday."
A win over Elche would not only allow Villarreal to stay in the race for Europe - it would also bring some joy to their fans, who have been unable to toast a home win since the start of February.
"We need to keep playing like we did against Getafe," added the goalkeeper, who is on loan at Villarreal from Atletico Madrid.
"The game is at home and we are really keen to win at home because it's been a long time since we last did that. We have to go out and give everything at our ground and get three more points, if we do that we'll take a big step forward."
Mexico international Giovani Dos Santos has been ruled out of the game with a hamstring injury, which he sustained just five minutes after coming on as a substitute in Villarreal's 1-0 win at Getafe on Thursday, while defender Jaume Costa has had a yellow card rescinded, meaning his suspension has been dropped and he is free to face Elche.
The Alicante side held Champions League-chasing Athletic Bilbao to a 0-0 draw on Tuesday to move one point further away from the drop zone, but they could end up in the bottom three should they lose at Villarreal and other scores go their way.
However, coach Fran Escriba offered a note of optimism in his pre-match press conference.
"We need to win and we are very aware that we can do that," he said.
"We don't have a big enough points cushion to be calm about our situation, so there's no way we could relax."