The Welsh side secured their top-flight status next season following Tuesday night's 0-0 draw with Charlton Athletic.
"For him to see that and for his son to play a part in promotion - that makes it even more special. It hit home to me he will die a happy man," the Daily Mirror quotes Bellamy as saying.
"I have lost count how many games I used to go with him, on a Tuesday night against some team; pulling me to the side, leaving 10 minutes before the end, and saying we would never go back. Then on the Saturday we would be there again.
"It has been so many years for this club to be in the top-flight. Everyone has been so desperate for it. It was an emotional night."
Bellamy signed for Cardiff last summer following a season at Liverpool.