László Régi started his football career in the team of Terézvárosi TC where he played in the first team at the age of 16 and was invited into the national youth team. In 1932 he moved to BSzKRT, where he soon became a key player of the team. Until 1937, he was the number one goalkeeper of BSzKRT but, after a series of military calls, he was not able to participate in training and therefore played only in some friendly matches. But his performance over the four years was enough to be a member of the Hungarian amateur team 10 times and to represent the Hungarian colors at the Berlin Olympics.
He finished his active sports career in 1945, but he remained loyal to his affiliation, and continued to work there as a goalkeeper trainer.