He came on as a late second-half substitute in a goalless draw with ČSK Čelarevo at home, thus breaking the record of Dejan Petković and becoming the youngest ever player in the club's history.

[6] He netted a brace on his debut for the club on 14 September 2013, thus giving his side a 2–0 home league win over Spartak Subotica.

[16][17] On 20 April 2024, the Ferencváros–Kisvárda tie ended with a goalless draw at the Groupama Aréna on the 29th match day of the 2023–24 Nemzeti Bajnokság I season[18] which meant that Ferencváros won their 35th championship.

[21][22] Pešić has represented Serbia under-19 at the 2011 UEFA European Under-19 Championship, where the team were eliminated in the semi-finals against the Czech Republic.

On 15 November 2016, Pešić made his full international debut for the senior team, playing in a second half in a 2–0 friendly defeat against Ukraine.