Atletico are fourth in La Liga with 12 games left to play after Valencia were dispatched courtesy of a brace from Antoine Griezmann and a Kevin Gameiro strike.
Simeone's men had drawn at Deportivo La Coruna and lost at home to Barcelona in their previous league fixtures, and the coach was satisfied by his players' response.
He said: "Having played on Thursday, we responded very well physically and mentally and we saw what had to be done. The team struck in the first half and we could have scored more.
"Apart from the defeat against Barcelona, we have been playing well, we have maintained a line, and we are trying to become stronger with each match.
"Each match is a final and we will see who has the most strength."
Simeone paid tribute to his players after they ensured his 200th game in charge of the club ended in victory.
"I honestly never imagined getting to 200 games with the club," he said. "I am happy in the place where I am, and I have a group of players who have been competing with heart for five years despite difficulties.
"Today they have demonstrated that the team is committed. I hope we can achieve the consistency that we have been asking for."
Goalscorer Griezmann said the Atletico players were happy to have Fernando Torres watching from the stands after the striker was hospitalised due to a head injury sustained against Deportivo.
He said: "I'm very happy and pleased with the performance. The work has to carry on. We wanted the three points and we wanted to play well and that's exactly what we've done.
"We're very happy and we're happy Fernando is with us and hope he's back as quickly as possible."