Head of development Mark Wright also requested his contract be terminated by mutual consent, to which the club have agreed.
The Sandgrounders lost 3-0 at Nuneaton Town on Saturday and have conceded 19 goals in five games, including an FA Cup second qualifying round defeat.
Director Ian Kyle said: “We would like to thank Mark & Alan for their hard work and dedication over the last few months, however, on the back of recent performances on the pitch, The Chairman & Board of Directors felt it in the best interests of the club and the Management team to move in a different direction.
“Mark & Alan were an instrumental part of our early season success, and we would like to extend our thanks and best wishes to them both and wish them every success in the future.”
The club will now begin the process of advertising the positions of First Team Manager and First Team Coach, and engage in a thorough and measured approach to those appointments.
In the interim, Club Captain Steven Schumacher and Goalkeeping Coach Iain Turner will take charge of first-team matters.
For more coverage, reaction and some of the best moments from games going throughout the season, head to our social media channels on Twitter, Facebook and now Instagram.