Nish was placed in charge of the side at Central Park in June after Jimmy Nicholl’s resignation when the team had finished bottom of the Championship.
The 35-year-old was still playing and substituted himself on in the last game of the season on Saturday to no avail as they went down 2-1 on aggregate to Gus MacPherson’s men.
Nish’s contract, an 18-month deal he originally signed to play for the club in the second tier, concluded this summer and the club have decided not to renew it.
Assistant manager Jason Dair will be acting caretaker manager until the board appoint someone to the vacancy.
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