Skevofilakas started his football career in 1955 at one of his neighborhood teams,
Eleftheroupoli, where in 1961 he was transferred to
AEK Athens at the age of 21. He played in the midfield positions with and especially as a
wide midfielder. His official debut with the yellow and black jersey was at
Rizoupoli Stadium on 9 September 1961, in the victory of AEK over
Egaleo by 8–0, where he provided three assists in the two goals of
Nestoridis at the 40th and 43rd minute and a goal of
Stamatiadis at the 65th minute. Skevofilakas won 3 championships and 2
Greek Cups, while he was a member of the team that played in the
European Cup quarter finals in 1969 against
Spartak Trnava, losing by a margin the opportunity to face
Johan Cruyff's
Ajax in the semi-finals. The intention of the club's then manager,
Branko Stanković to renew the club's roster, brought Skevofilakas to leave AEK among other players, in 1972 and move to
Atromitos. On 21 May 1973, Skevofilakas alongside
Balopoulos, Psychogios and
Kefalidis, who were all released from AEK and signed for Atromitos, started in the game against their former club at
Peristeri Stadium, where the match ended with a 1–0 victory for the hosts. It was the first time that they played against AEK, while
Lakis Nikolaou, made his maiden participation against his former club, with the yellow-blacks. He retired as a footballer in the summer of 1973, at the age of 34. ==International career==