He started his professional career in Army team Tankista Prague (1954–1955) and kept on in Spartak Košice (1956), Tatran Prešov (1957–1960) and ended in Jednota/VSS Košice (1960–1966).
Felszeghy overall made 141 appearances and scored three goals at the Czechoslovak First League.
On 13 November 1955, Felszeghy earned his only cap for the Czechoslovakia national football team in a 0–3 defeat against Bulgaria at Vasil Levski National Stadium.
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