Haye was floored twice in the third round and the fight was waved off in the fifth after the 37-year-old toppled to the canvas again, Bellew producing a second successive stoppage victory at the O2 Arena.
The former unified cruiserweight world champion has not confirmed whether he will hang up his gloves following his second defeat to Bellew, but long-time friend Froch is adamant that Haye should not continue in the ring.
"There is only one answer about his future: David Haye should retire. 100%," Froch wrote for Sky Sports News. "Straight after the fight, I just went to see his mum and dad and told them to tell him to do the right thing and finish.
"I don't like saying it but this has to be the end for him now. We have been friends for a long time and we have all been thrilled and entertained by his achievements, but I don't want to see this happen again.
"People shouldn't forget that as a boxer he has given us more than we ever expected. David did things beyond the call of duty. He was the undisputed cruiserweight champion of the world and then, to go on and win and be a heavyweight world champion, that says it all. But that has to be it now."
Haye has taken part in 32 fights, winning 28 and losing four.