 On 14 August 2011, Da Costa made his debut in Russia against Volga Nizhny Novgorod in a 0–0 draw and also on his debut, he received a yellow card.On 28 August 2011, he provided assist for Felipe Caicedo to score the only goal in the game to beat FC Kuban Krasnodar 1–0.On 10 September 2011, he scored a brace and his first goal in Russia to beat defending champion FC Zenit Saint Petersburg 4–2.