The 30-year-old international passed away on Friday of a suspected heart attack after complaining of chest pains while training with his club.
Carter complained of chest pains after training with his club, Defence Force, and was taken to the hospital in his native Trinidad but later passed away.
The Caribbean forward, who played for the same team his entire career, was capped 25 times by his country.
TTFA general secretary Sheldon Phillips expressed his disbelief and sadness at Friday's tragedy.
"Words are inadequate to describe the emotions currently felt about the passing of Kevon," Phillips said in a statement.
"The young man had a quiet resolve about him and bounced back from a horrific leg injury to once again earn a spot on the national team. The entire football family is in mourning and our thoughts and prayers are with Kevon's family and teammates."