Hafey coached Malthouse after his mid-season arrival at Richmond in 1976, but the pair formed a friendship that would last the rest of Hafey's life.
"He was an amazing man," Malthouse said.
"Tommy coached me for half a season but that half a season established a bond that was alive and well up until this afternoon."
Speaking after his side's five-goal win over St Kilda, Malthouse said he owed a great debt to Hafey.
"You get blessed when your first two coaches are the late Allan Jeans and now the late Tom Hafey," he said.
"They teach you so much about life and so much about football.
"And I think that's the secret to it. They're not just football coaches."
Malthouse said Hafey would be remembered as a great man.
"Not only a great coach, but a great teacher of men and boys."
Both men coached four AFL/VFL sides, with Hafey winning four premierships; Malthouse three.
