On 28 September 2013, Puskás surprisingly beat Ferencváros 3-1 at home on game week 9 of the 2013-14 Nemzeti Bajnokság I season.

[4] On the 30th matchday of the 2015–16 Nemzeti Bajnokság I season, Robert Jarni was dismissed due to the defeat against Békéscsaba 1912 Előre at the Pancho Aréna on 16 April 2016 resulting Puskás Akadémia's last position and relegation for the first time in history.

Pintér left Mezőkövesdi SE, playing in the 2016–17 Nemzeti Bajnokság I season, for Puskás Akadémia.

[6] On 21 May 2017, Puskás Akadémia won the 2016–17 Nemzeti Bajnokság II season after a goalless draw against Ceglédi VSE in Albertirsa.

[7][8] On 12 June 2017, András Komjáti, previously manager of Vasas SC, was appointed as the club director.

[15] On 7 April 2019, Radoki was replaced by András Komjáti after a shocking defeat (0–4) at home against Kisvárda FC.

In the first round, Puskás drew with FC Inter Turku[18] and beat the Finnish team at home.

[20][21] On 21 July 2022, Puskás lost 3–0 against Vitória S.C. in the first leg of the second round of the 2022–23 UEFA Europa Conference League at the Estádio D. Afonso Henriques in Guimarães, Portugal.

[28] On 28 July 2024, Puskás started the 2024–25 Nemzeti Bajnokság I with a 2–1 victory over Újpest FC at the Szusza Ferenc Stadion.

[30] On 8 August 2024, Puskás beat FC Ararat-Armenia 1–0 at the Vazgen Sargsyan Republican Stadium in Yerevan, Armenia.

In the second half, Fiorentina could equalize the result thanks to Lucas Martinez Quarta and took the lead in the 75th minute thanks to Moise Kean.

[46][47][48] As of matches played 22 August 2024 Note: Flags indicate national team as defined under FIFA eligibility rules; some limited exceptions apply.

Note: Flags indicate national team as defined under FIFA eligibility rules; some limited exceptions apply.