Challinor felt they should have been awarded an early penalty following a clash in the box between the Spireites’ Fraser Kerr and opposition striker Scott Quigley.
Referee Scott Tallis apparently admitted it was a foul but that he did not award the spot-kick because he did not believe Quigley was going to get to the ball, which Challinor said was ‘irrelavant in my eyes.’
And with Town leading two-nil in the first-half, the hosts thought they had pulled a goal back through Ash Palmer’s header but it was ruled not to have crossed the line.
Meanwhile, Chesterfield felt hard done to when Jeff King was shown a straight red card just after the break for a tackle on Will Collar. That swung the game in County’s favour and they scored twice to level.
The final result means the two sides are still separated by just one point at the top of the table.
"A few decisions did not go our way and maybe from their side of it they will say decisions went our way in the second-half,” Challinor said.
"In the second-half, a big decision has not gone for us because it is a red card but that changes the momentum of the game.”
On his team’s overall performance, Challinor was disappointed with the first-half display and admitted he would have been happy with a point at half-time.
He explained: “It was poor from us in the first-half in terms of bad decisions and not dealing with threats which allowed them to play the game they wanted to play it.
"We conceded two poor goals. I thought in the first bit of the game the back three did not deal with their front two.
"We spoke at half-time about showing character and us still being in the game at two-nil if we went about things better in the second-half and were braver in terms of our decisions and I thought we were.”
With the scoreline level but all the momentum with the Hatters, the game was only heading one-way but Town regrouped and showed great spirit to see out 10 minutes of added time.
Chesterfield can regain top spot with a win against Weymouth on Saturday because Stockport are in FA Trophy action.
Challinor added: "I am disappointed with our last 20-30 minutes, I thought we could have been better with our simple passes in order to cause them more problems but credit to them (Chesterfield), they have dug in there.
"They (Chesterfield) are delighted with their point and I suppose at half-time if I had been offered a point I would have been delighted with it as well.
“If I had been in their dugout, coming away from home to a team who had won 10 on the spin and having to play the last 35-40 minutes with 10-men and conceding the equaliser with potentially half an hour to go, then I think I would be pretty pleased with a point I think.”