The Spireites were tipped as promotion candidates but for a second season running, they failed to make the play-offs and a section of supporters protested for Richardson's sacking during the Saltergate clash.
Richardson is out of contract next month and must now wait to find out if he is to be offered another tilt at promotion next season.
He admitted: "We have not been good enough to get promoted this season.
It's the second time on the trot we have narrowly missed out.
"I have been in charge for those two seasons and it's quite simple in some
people's eyes where the blame lies.
"We have let too many points slip this season, that's been the real nail in our coffin but I would like to thank all the supporters for their support, they are entitled to their opinion."