He became a first-team player in January 2002 at the age of 17 and debuted in spring 2002, receiving a red card in his first match.

[3] After going on trial with FC Bunyodkor in February 2014,[4] Kopúnek went on to sign for Ravan Baku of the Azerbaijan Premier League in March 2014.

[6] Kopúnek signed a half-year contract with the Synot liga club FC Zbrojovka Brno on 20 March 2015.

[8] He scored his first international goal against Cameroon on 29 May 2010 and was subsequently named to the Slovakia squad for the 2010 FIFA World Cup.

[9] On 24 June 2010, coming on as a substitute, he scored Slovakia's third goal with his first touch of the game in their group match against Italy which ended 3–2 and eventually sent the Italians crashing out of the FIFA World Cup 2010.