Atletico Madrid striker Costa played the full 90 minutes in his home stadium as Spain claimed a 1-0 win.
Brazil-born Costa was just delighted to finally make his bow for Spain after much debate over his international future.
"I am very happy to have made my debut with the team and to have won the match," he told Globo Esporte.
"I'll keep doing my job at Atletico to have chances to be in the national team. I know the first game isn't easy. I'm happy, but I know I can give much more."
Spain boss Vicente Del Bosque insisted he was happy with how Costa played.
"We are pleased with Diego. He has integrated very well into the team, we are happy with his debut," he said.
"He looked stable taking into account it was his first game, but once he loosens up I'm sure he'll bring a lot more to the team."