Spireites boss Paul Cook was left feeling hugely disappointed, despite seeing his side win 3-1 at Fleetwood.
The victory was to no avail as Bradford City beat Burton Albion 1-0, putting them four points ahead of Chesterfield with only one game remaining.
Two goals from Marc Richards and a header from Armand Gnanduillet put Chesterfield three-nil up before Andy Mangan pulled a goal back for the hosts.
Speaking to Spireites Player, Cook admitted he was deflated but thanked the fans for their support.
He said: “I’m hugely disappointed. We’ve been inconsistent and that’s been our downfall. Overall, the league tables don’t lie.
“I’m absolutely devastated. I’ve never felt so sick after winning a game. We missed out today, but you’ve got to take your hat off to our support. I can guarantee our supporters that this club will get the success it deserves.
“Our club is run by a really good chairman and backed by a fantastic board. They won’t leave a stone unturned until this club gets some kind of success. They will get what they deserve.
“The positive for us today is our support. For people to travel like that, and believe, like they do. I take my hat off to them. Coming out to see that support today was very special.”
Gnanduillet came on after Richard Brindley went off with a suspected hernia problem and the manager was pleased with the Ivorian and his strike-partner Marc Richards.
Cook added: “Armand gives us that physical presence up front which helps us. He offers us something different and he’s a little bit unique in that he’s so new to football.
“He does some things wrong, but he doesn’t half do some things well and if he does stay with us after the summer, we will work so hard to get it right for these supporters.
“Marc has been stop-start all year. I think you can see that, now and again, Marc needs that support. The balance of the team must be right. Sometimes, when we play 4-4-2, we don’t really have enough wingers and put enough balls in the box, so I always think there’s something wrong with what we’re trying to do.”
Cook revealed that Jack Lester will captain the side in his farewell appearance against Exeter next weekend. He said: “One thing we can look forward to next week is a very special day for Jack Lester.
“He will captain the side and will lead us out, and I want the ground to be full. We can give him the special ovation I know he will get. He’s been such a special player for us, but we can focus the week now on Jack Lester.”