Las Palmas won 1-0 on Saturday, with Javier Munoz scoring in injury-time.
Simeone said afterwards: "If we had any chance of winning LaLiga, we had to put up perfect numbers, but we didn't do that today. The goalkeeper made the most of the first-half chances.
"In the second half, the game started dull and boring. We couldn't do what we wanted, and the goal exemplified what had been seen.
"We've been here for 14 years, and we're going to cherish what we've done. We'll keep looking for people who will help us."
Simeone also said, "It's not an attitude, it's just that we played poorly. I made the substitutions so the team could find a new path, which they didn't. Players have been good when they came on other times, but not today.
"In the first half, we did well. But in the second half, we played poorly. We have to try to improve that aspect. Being at Atlético is wonderful, and we'll take care of it like we have these past 14 years."