Since scoring on his debut against Trinidad and Tobago in 2007, Costly has been a standout performer for the Honduras national football team helping the "Catrachos" reach the semi-finals of the CONCACAF Gold Cup in 2009 and 2011. He is the Honduran national team's second-top goalscorer of all-time in Gold Cup matches, scoring eight goals, including a hat-trick against Grenada in the 2011 tournament.