Atletico salvaged a point at Vallecas Stadium thanks to Conor Gallagher's strike after the break following a sloppy first half in which Isi Palazon had put the hosts ahead.
Simeone's side slipped to fourth place with 12 points, six behind leaders Barcelona and two shy of second-placed Real Madrid, whom they face next Sunday.
"In the first half, we had more scoring situations than gameplay. Then we saw intensity, involvement, a lot of people in the opposition's half, attacking in different ways," Simeone told reporters.
"I always focus on the positive, on the second half. We conceded a goal but we also had chances to score... We could have won the game.
"(I look at the league race) with the same enthusiasm to go game by game, to face each one as if it were the last one. We are on that path."
Atletico's big-money signing Julian Alvarez went close to finding the net after 20 minutes but hit the woodwork, with the Argentine striker yet to find his goalscoring form, with one goal in six games this season.
However, Simeone is confident that Alvarez and the rest of his forwards will find the sharpness they have been lacking.
"We are convinced that the goals will come. The problem is when the strikers don't have goal situations," the Argentine manager said.
"(Today) I liked Julian playing on the left, with a lot of effort. (Angel) Correa came on very well... (Antoine) Griezmann put the team in the opposition half. I was happy with the second half."