The 31-year-old Scot was one of two players - fellow keeper Michel Kuipers the other - offered new deals by the Red Devils, who secured back-to-back promotions after finishing third in League Two this season.
But Shearer, who pulled off several outstanding saves to help clinch Crawley automatic promotion with a 1-0 last-day win at Accrington, told the Crawley News: "They made me an offer but I've got a family to think about and the deal they offered me didn't suit me.
"I felt they thought less of me than what I think of myself."
Shearer, who joined Crawley from Wrexham in December 2010, made 30 first-team appearances for the club this season.
