Their only victory this season was a 2-0 Carling Cup success against Tranmere last month.
"This difficult decision takes nothing away from his wonderful achievements which transpired in the club enjoying an extended stay in the Championship together with three wonderful trips to Wembley," the statement added.
"We would like to express our sincere thanks to Alan and we are sure that everybody connected with the club will respect him for his magnificent achievements whilst manager."
Assistant manager Stuart Watkiss has assumed first-team duties on a temporary basis at Blundell Park.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.