Musta was a product of Partizani Tirana academy, and was promoted to senior squad in 1979 and went on to play there until 1991. In January 1991, he scored from the penalty spot in a league match against Luftëtari. He left Albania in 1991 like many Albanians following the fall of communism, joining Romanian side Dinamo București. He failed to establish himself as a regular at Dinamo because of the two Romanian international goalkeepers, Florin Prunea and Florin Tene.