Ronnie Jepson, the assistant manager, first-team coach Mick Docherty and vice-chairman Andrew Watson have also left the club.
Ternent's exit comes a day after John Ward was sacked by Carlisle United. The Championship side Watford have also sacked Aidy Boothroyd.
Ternent, 62, had been allowed to sign 11 players in the summer - including Jim Goodwin and Andy Butler on free transfers from Scunthorpe.