Jamie Grimes headed the Spireites in front on 16 minutes but two late goals from Dior Angus turned the scoreline around at Moss Lane on Saturday.
Parkinson said: “Any time you can go toe-to-toe with a Chesterfield, any time you can get a victory against the title contenders, that is what everyone is calling them and rightly so, with the size of the club and the investment they have put in there, the football they play, it is a fantastic day.
“It is a great occasion for us, a big feather in our cap, and one that was thoroughly deserved I felt on the day.
“In Paul (Cook) they have got a seasoned manager, Danny (Webb) his assistant is superb as well, he speaks really well, comes across great. They are a really good outfit.”
Parkinson was full of praise for Chesterfield but he was delighted how his side went ‘toe-to-toe’ with them, particularly in the second-half.
He said: “People will rightly stand off Chesterfield at times, but we didn’t, we went toe-to-toe with them and I felt we got our just rewards for that.
“They (Chesterfield) have scored a lot of set-pieces this season so we knew they would be good at it and you could see without us playing a third centre-half we were not as big.
“In the first, they (Chesterfield) were on top, they had territory, I don’t think there was much goalmouth action, I don’t remember Ethan (Ross) having much to do or their keeper.
“There were a few words said at half-time because we knew there was more to come from our group, I don’t think we worked as hard as them and I don’t think we showed our quality in the final third.”
He added: “Everything we asked of the lads at half-time, they came through and that is why they got the result because they stepped it up and showed what good players they are.
“What we have done today should not be underestimated.”