Alsop, 20, struck 117 not out on the second day of Hampshire's Division One match against Surrey at The Oval.
"I want to dedicate my century to Michael," he told BBC Radio Solent. "He helped me a lot through the academy.
"I would like to thank him for everything he has done to help my game. Everyone is with him."
Left-hander Alsop continued: "I've gone to him for all types of advice, things about batting mostly, and we're good friends off the field.
"To see what he has gone through has been pretty tough for everyone, on him and the club.
"I would like to thank him for everything he has done to help my game. Everyone is with him."
Opener Carberry, 35, played the last of his six Tests for England in January 2014 and last played for Hampshire in a T20 match on 8 July - six days before his diagnosis.
Hampshire batsman Tom Alsop has dedicated his maiden first-class hundred to team-mate Michael Carberry, who was diagnosed with cancer in July.