Ferguson, 76, remains in intensive care following emergency surgery on the haemorrhage on Saturday, but United said the procedure had gone "very well".
Jones was signed by Ferguson from Blackburn Rovers in 2011 and was part of the squad that won the Scot's 13th Premier League title in his final season before retiring in 2013.
"(I am) just devastated, absolutely devastated," Jones said.
"He is such a legend in my eyes. He is the one who brought me to the club and gave me that opportunity to play for one of the biggest clubs in the world. He's taken me under his wing like a father and it was shocking."
United thanked well-wishers from around the football world on Sunday as the esteem with which Ferguson is held as one of the greatest managers in history was evidenced in the calibre of players and coaches wishing him a speedy recovery.
Arsene Wenger, Jurgen Klopp and Pep Guardiola were among those to express their admiration for Ferguson, who won 38 trophies in all in just over 26 years in charge of United.
"It's sad, but I know his character," added Jones. "I know he has that fight in him. Hopefully he'll recover well."
"He has got all his family and friends around him, the support from all the players and staff at Man United and football around the world.
"When something like that does happen it's nice that the football world comes together and shows support and we are all rooting for him. I'm sure he will be fine."