In December 1989 he was signed by Jim Leishman for Scottish team Dunfermline Athletic for £550,000 which is still the club's record transfer fee.

Kozma made his debut in a goalless draw against Ipswich Town in the fifth round of the FA Cup,[2] but never looked like breaking into the first team at Liverpool.

His poor performance at Liverpool earned him in 2007 the dubious success of being rated by Times Online as the fourth worst ever player to play in the Premiership.

He subsequently signed for Austrian amateur side Ostbahn XI Wein and Hungarian lower-division teams Budafoki MTE and Rákosmenti KSK.

[8] After just five months, Kozma left his position at the club in October 2013, being sacked altogether after initially being transferred to the role of video analyst instead.