Missing top scorer Diego Costa and playmaker Arda Turan through injury, Atletico took the spoils courtesy of Raul Garcia's 14th-minute header - ensuring another weekend at La Liga's summit with six games remaining.
But they were forced onto the back foot for for long periods after the interval as Villarreal produced an assured display in the hope of boosting their European ambitions.
"It's amazing the hard work done by my players," said Simeone. "There are no words to congratulate them for this and also for this commitment to the club.
"It was a tough game. Despite the goal, we struggled in the first half as we couldn't find ourselves between the lines as we wanted. But we did get a goal from a corner kick.
"In the second half, Villarreal were better than us in terms of possession. They had the ball more, but this didn't mean they created chances, nor did we counter-attack to show we were not only defending. This is a vital victory."
Atletico's latest win moves them to 79 points, already three more than the tally that earned them third place behind Barcelona and Real Madrid last term.
And if they are to hold off the two giants of Spanish football for a first league title since 1996, Simeone believes the club's fans - who were in fine voice once more at Vicente Calderon on Saturday - have a vital role to play.
"Maybe (it is) because I know this club very well, but the fans have to be aware of how important they are for the team - this is something I have no doubt about," added Simeone.
"We've done a great effort so far after so many games. And when they cheer us you can tell in the atmosphere.
"It cheers you up, it makes you feel stronger and it gives you the strength you need to keep competing. And that's exactly what they did today.
"Usually, people wonder why we are Atletico fans and this is the reason. We are passionate, we work, we have humility. And if we have to suffer, then we will. We have no problem with it."
