The 25-year-old made his debut for the world and European champions in Wednesday's 1-0 friendly victory over Italy at Vicente Calderon.
Costa's involvement with Spain has courted much publicity after he opted to play for his adopted nation over the country of his birth, Brazil.
He has previously featured in two friendlies for his homeland, but was allowed to switch allegiance as he has not played an official FIFA fixture for Brazil.
While some managers bemoan their players being involved with international sides, Simeone has embraced Costa's involvement, believing it will benefit his team in the long-term.
"I think Diego has some qualities which suit any team," the Argentinian said.
"It's clear also that if he had the chance of working with Spain, our team would take some advantages because he will grow as a player and he will improve here too where we need him as well."
Atleti travel to Celta Vigo on Saturday on the back of a morale-boosting 2-2 draw with city rivals Real Madrid last weekend.
It took a late goal from Cristiano Ronaldo to ensure Real remained at the top of La Liga, while Atletico are just three points adrift in third.
And Simeone stressed the importance of building on that performance.
"I told the players after the match (against Real Madrid) that to me we did a really good match," he added.
"But now we are facing an important match against a really good side and we will have to be ready for this match."
