[6] On 3 January 2015, Šatka made his senior debut in an FA Cup match against Leicester City, which his team lost.

[7] Šatka joined League Two club York City on 29 January 2016 on a one-month youth loan,[8] and debuted on 6 February as a 58th-minute substitute for Matty Dixon in a 2–0 away loss to Northampton Town.

[9] Šatka returned to Slovakia to join Dunajská Streda on 10 January 2017 on a six-month loan deal.

[12] Šatka agreed to sign for Ekstraklasa club Lech Poznań on 29 June 2019 on a four-year contract, only joining the club in mid-July after Dunajská Streda's tie in the 2019–20 UEFA Europa League first qualifying round.

[15] Šatka was listed as an alternate in the senior team for the two qualifying matches against Slovenia and England on 1 September 2017.