Fans called for his head during the match, and the former Wimbledon and Wales manager called time on his ten month stint with the club.
A statement from the Cheltenham board read: "The Board wishes to thank Bobby for his hard work, enthusiasm and commitment.
"We feel that Bobby has been treated in an appalling manner by the local media.
"That treatment is not justified for anybody, let alone someone of the calibre of Bobby Gould, who has done so much throughout his football career."