Alexopoulos began his career in the academy of Panathinaikos and wore the green jersey for 7 years.
Alexopoulos made 30 appearances in Greek League and also scored 3 goals until he was seriously injured.
On 16 April 2008 he returned to full training and was expected to be 100% ready for the next season.
In the 2008–09 season he returned and made 12 appearances serving as back-up choice to Daniel Majstorović and Sotirios Kyrgiakos.
In the summer of 2010 Alexopoulos joined Ergotelis as a free agent, where he finished his career a year later.