All attention was on the Brazilian-born striker as he lined up for Vicente Del Bosque's side for the first time, but the limelight was stolen by his Barcelona rival Pedro, who netted the only goal of the game to beat Cesare Prandelli's men.
Costa, though, said he was delighted to have represented la Roja and insists this is only the beginning of his journey with the national side.
"I am very happy to have made my debut with the team and to have won the game," said the 25-year-old.
"I'll keep doing my job at Atletico to have chances to be in the team. I know the first game isn't easy. I'm happy, but I know I can give much more."
Del Bosque was full of praise for the Atletico Madrid man and insisted he did well on his first outing with the squad.
"We are pleased with Diego. He has integrated into the team very well, we are happy with his debut."
Spain have two more friendlies against Bolivia and El Salvador before their opening World Cup match against Netherlands.