Dean Smalley gave Chesterfield a 16th minute lead on his return from suspension and despite late pressure from the Bantams, his side managed to hold on to all three points.
Taylor said: "We looked a bit too nervous in the first half because of the situation we are in. I'm not sure that our players look forward to home matches at the moment but that is something they have to overcome because they are playing in front of a good crowd.
"In the second half, after James Hanson came on, we looked as if we could handle everything better and get a goal but it never came.
"Originally I was told James would be out for four weeks but his injury wasn't as serious as we thought so he started out on the bench and came on.
"We needed a bit of luck but Chesterfield are top of the table and a very good side. I was disappointed with the result but not the performance. We didn't look that far away."