Jordan Bowery hit a last-gasp equaliser for the League Two leaders as the Bantams' run of four consecutive defeats came to an end.
Danny Whitaker's early strike put the Spireites ahead before Dave Syers' equaliser and James Hanson's effort put Bradford 2-1 up.
Yet Bowery struck at the death to salvage a point and Sheridan said: "We definitely deserved to get something out of the game.
"We left it very late but I thought we started the game well and if we had kept hold of the lead a little bit longer we could have gone on to win comfortably.
"But full credit to the players, they showed character and I'm very pleased with the way we played second half, we showed a lot of patience and belief that we could get back in the game and we did the right things."