The former England manager, 72, who arrived in south London four games into a disastrous start to the 2017-18 season following Frank de Boer's brief spell, will remain at Selhurst Park until the end of next season.
"It is incredible the appetite for the game he has got, unbelievable at that age," said Cahill. "It is incredible. He has been in the game for so long, in different countries, leagues and with national teams so there is not much he probably hasn't experienced.
"It is great for the lads that he has signed an extension, it is the stability for the club and players for next season.
"His drive to still be involved and still be hungry to come in every single day is unbelievable, it is crazy, I'm not sure that will be me!"