During the 1950s he was a fringe member of the team known as the Mighty Magyars and played alongside the likes of Ferenc Puskás, Zoltán Czibor, Sándor Kocsis, Nándor Hidegkuti and József Bozsik.

Despite this turmoil, the 1950s proved a successful era for club and it was while at MTK that Palotás, together with Nándor Hidegkuti and coach Márton Bukovi, pioneered the deep-lying centre-forward position.

On 17 May 1953, he helped Hungary clinch the Central European International Cup when he played in a 3–0 win against Italy at the Stadio Olimpico.

By 1953 Hidegkuti had established himself as the first-choice deep-lying centre-forward for Hungary and as a result Palotás missed out on the two prestige friendlies against England.

During the 1954 FIFA World Cup he scored twice in the group stage 9–0 win against South Korea and also played in the semi-final against Uruguay.