Career
Alexoudis played most of his career for OFI Crete and Panathinaikos Football Club. He played for Greece national team (4 matches/one goal), and was a participant at the 1994. From 22 November 1995 to 1 October 1997 he was at the top of the list for the fastest goals in Union of European Football Associations Champions League history, thanks to a goal he scored after just 28.46 seconds into Panathinaikos Football Club"s home match against Aalborg BK.