 In October 2010 da Costa was called up, for the first time, into the Portugal under-23 team for a game against Northern Ireland under-23 team on 12 October.In May 2014 Da Costa was named by coach Badou Zaki in the Morocco squad for the 2015 Africa Cup of Nations, to be hosted by Morocco.On 23 May, he made his debut for the "Lions of the Atlas" in a 4–0 win against Mozambique.