The result was Valencia's second defeat in a row, following an unbeaten run of four games, and sent them down to 11th in the Primera Division.
"We are all worried, upset and sad when we lose games, and there is a lot of disappointment among the dressing room because we are further away from where we want to be in the league," Djukic told a press conference.
Valencia have a chance to get back to winning ways on Wednesday, when they host bottom club Almeria, who have lost five consecutive matches.
The Serbian coach underlined the importance of his side obtaining a win to get the defeat against Villarreal out of their system.
"Whenever you lose it's always important that the next game comes around as soon as possible so you can get rid of the bad taste you have from defeat," Djukic said, "and we want to win so we can feel good about ourselves again."
He also expressed confidence that his team could start climbing the table.
"There is enough quality and strength in the team to turn this situation around," Djukic said.
Djukic will have to manage without his midfield talisman Ever Banega, who is suspended after accumulating five yellow cards in the first 10 games of the campaign.
Francisco Javier Rodriguez's Almeria side were beaten 3-0 by Real Sociedad in their last game, and are six points from safety as a result.
On the plus side for the coach, midfielder Suso returns after missing the defeat in San Sebastian with illness, and Cristian Pellerano is also back, after completing a suspension.
"We're going to try to get ourselves back on track and at home to Almeria is a good chance to do that," added Djukic.
But he warned that, despite the precarious position in the league table they occupy, the Andalusians would be no pushovers.
Djukic said: "It will be a difficult game, against a team that is strong on the counter-attack. It's a deceptive game. We need to be prepared and smart if we want to win it."