Richardson's contract expired at the end of the season but the Spireites decided not to renew his deal following another failed promotion attempt and the 40-year-old left his post on Wednesday.
He told the club's official website: "For the first half of last season we were as good as anybody and I honestly think in the second half of this season we've displayed that as well with the victories at Brentford and
Bury and coming to within five or 10 seconds of beating Wycombe.
"There have been lots of good days but they all get forgotten if you want to focus on what went wrong, which it's very easy to do."
He added: "There's no doubt I've made mistakes in both seasons. It's crucial you get the right players. I think we've had a lot of success in getting some good players here but I've made some decisions that I would probably change given the experience I've got now.
"I don't think I'm alone in that in terms of managers who say the same and it is a bit of a cliche but I do think I'm a better person and manager than I was two years ago."