Four people, named locally as Corey Price, Rhodri Miller, Alesha O'Connor and Margaret Elizabeth Challis, died after a crash on the A470 near Storey Arms.
A statement issued on the Bluebirds' official website read: "At this most difficult of times, our thoughts and prayers are with those affected by the accident, particularly the families and friends of those who lost their lives. We offer our sincere condolences to them.
"Rhodri Miller was a keen Bluebird and a season ticket holder at Cardiff City Stadium. Corey Price was a former academy player, representing the club over an eight year period from the age of nine years old."
James McCarthy, who worked closely with Price during the 2013-14 season in his role as academy manager, said: "Corey was a gifted footballer.
"He applied himself wholeheartedly to his football and academic studies, which made him extremely popular amongst his peers and all academy staff.
"He was a pleasure to have around and we were privileged to have played a part in Corey's footballing, academic and personal development.
"He will be sadly missed by all."
The club's academy have announced plans to pay their respects to the quartet with a minute's silence before kick-off at Tuesday evening's youth game against Newport.
skysports.com