On 27 August 2023, at home Ferencváros beat 6-1 Paks that has been biggest win in the Nemzet Bajnokság I, while managing the club.[7]
On 4 September 2023, he was sacked from Ferencváros and was replaced by former Inter defender, Dejan Stanković.[8][9]
In an interview with Nemzeti Sport, he said that he was surprised that had been sacked by Ferencváros. However, after two months he feels that he can start working again.[10]
On 19 October 2024, Debrecen lost 5-0 to Paks at the Nagyerdei Stadion. After the match, Máté said that he was not afraid of being sacked.[14] On 26 October 2024, Debrecen lost to Fehérvár 2-0 at the Sóstói Stadion.[15] After the match, Máté said that he would discuss his future at the club.[16]