Jordan Bowery hit a last-gasp equaliser for the Spireites 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.
Bowery struck at the death to deny Bradford but Taylor said: "There were a lot of plusses, tremendous work-rate from the players and I felt for them at the end because Chesterfield are the league leaders and are the best team so to come here and nearly get a win is a great performance.
"The effort the players put in was fantastic but again there are little things we have to learn from it. In the end it's a poor goal, I think most defences try and defend outside the box and maybe we were a little bit too deep.
"I think we know the situation we are in. We know we have underperformed and the position in the league is not good enough for what we want but no-one is going to give us anything. We have to earn it and everything the players did they earned and I'm really sick for them that it's not any away win."