The Bootle-born centre-half is set to make his final Reds appearance against Queens Park Rangers at Anfield on Sunday before calling time on his playing career.
Drogba first faced Carragher in the Uefa Cup fourth round with Marseille in 2004, before the Chelsea forward came up against the defender 21 times in the Champions League, FA Cup, League Cup and Premier League.
And the Ivory Coast international admitted he was always braced for a tough encounter when Chelsea took on Liverpool with Carragher, 35, marshalling the Reds defence.
“Jamie is an icon – a Liverpool icon,” Drogba told Liverpool’s website.
“16 years at the club, he has been the captain and a true leader. I think even now, he is still the leader of the team.
“He did a lot of things for the club, including winning the Champions League.
“I played a lot of games against him and it was always a battle.
“When I thought I’d won the duel, he’d be there again, but it was always in a good spirit.
“That’s what made him a great player.”