The experienced England striker was ruled out of their match against Arsenal with injury, and his absence was sorely felt.
Sunderland clearly lacked a finisher as they fell to a 3-1 defeat at the Emirates Stadium, and Allardyce admits that nobody else in his squad is like Defoe.
“You can’t coach finishers, all those coaches who say they coach finishing are lying,” Allardyce said.
“Finishers are finishers. Our natural finisher is Jermain Defoe.
“All the other lads can score goals but they’re not natural finishers. Jermain is.”
Defoe is expected to return to Sunderland’s team for their next match against Watford, and that will be a major boost.
The former Tottenham Hotspur man has been in excellent form throughout the season so far, and he has already racked up seven goals in all competitions.
The service Defoe has received will increase now that Allardyce is in charge, too, as the team have improved considerably in recent weeks.
Although the Black Cats remain in the relegation zone, they have still shown signs of encouragement, and there is genuine hope that they will move away from trouble over the coming weeks.