Antoine Griezmann’s 25-yard free-kick in the 15th minute was enough to secure a 1-0 victory for Atletico at the Vicente Calderon on Sunday.
Next up for the men from the capital is a tricky trip to Sevilla, while Las Palmas will hope to pick up their first points of the season when they host Levante.
Simeone said it was important for Atletico to improve their play in the attacking third after needing the free-kick to break through.
Radamel Falcao and Diego Costa both enjoyed fine spells at the club before heading for pastures new and Simeone says Martinez – who joined from Porto this summer – has the necessary quality to perform in Spain. Using the “Ronaldo technique’ of drilling through the ball, the deflection baffled Raúl Lizoain in the Las Palmas goal and Atleti took a 1-0 lead”. Defender David Simon had made a late, curling run to the back post and found himself completely unmarked as the ball fell.
Atletico goalkeeper Jan Oblak had to scramble to clear his line in the 72nd minute after the home side couldn’t clear a corner.
Atletico’s Jorge “Koke” Resurreccion went close to widening the winning margin when he sent a free kick off the post in the last minute.
The other game between Deportivo La Coruna and Real Sociedad also ended 0-0.
Malaga and Sevilla kicked off the new Spanish league season on Friday with a a 0-0 draw.
First, Griezmann flashed a snap-shot narrowly wide before Tiago climbed highest to meet a Juanfran cross from the right, but failed to direct his header on target. Although there were new players, the overall attitude of the team did not change.
Saturday saw a series of woeful misses from inside the area.
It was then Rayo striker Manucho’s turn to lament his own howler in the second half when he turned Patrick Ebert’s low cross past the wrong side of the post.