Allardyce managed the pair at Crystal Palace and West Ham United, respectively.
Benteke and Carroll were managed by Allardyce at Palace and West Ham respectively, becoming focal points of the 64-year-old's teams.
The former scored in impressive nine goals in 22 games during Allardyce's Eagles reign - five fewer than the latter managed in 57 for the Hammers under the former England boss.
But Benteke has struggled since Allardyce left, finding the net on three out of 35 occasions, and is currently nursing an injury which has kept him out since September.
Asked what the problem has been with him, Allardyce told Thursday's Alan Brazil Sports Breakfast show: "I don’t know. He’s been out a long time.
"Christian Benteke was one major reason we stayed up, because he scored more goals than everybody else - scored 15 league goals (all season).
"You cross a ball for Christian Benteke, on his head, and he is - I thought Andy Carroll was really, really good at West Ham, but Christian Benteke was actually better.
"You know what ball he liked best? Stood up. Not the bender or the whipper. Just stand it up on the far post, he was terrific.
"You can say he didn’t work hard enough outside the box, and it was a lot of money that Palace paid, but he was goals."
Benteke is being tipped to return for Crystal Palace, who have slid dangerously close to the Premier League's relegation places, at the end of this month.
Crystal Palace or West Ham United's - whose centre forward would you rather have?
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