Karagkoutis started his career with the Greek club Panionios, at the age of 16.

With the Greek Under-16 junior national team, Karagkoutis won the gold medal at the 1993 FIBA Europe Under-16 Championship.

With the Greek Under-19 junior national team, Karagkoutis also won the gold medal at the 1995 FIBA Under-19 World Cup.

Karagkoutis also played with the senior men's Greek national team at the 1998 FIBA World Championship, where Greece finished in 4th place, and at the 1999 FIBA EuroBasket, where Greece also finished in 4th place.

He represented Greece 25 times at the senior level, and scored a total of 100 points.