James Hanson put the Bantams in front after just four minutes but Delroy Facey and Gavin McCallum hit back for Lincoln to condemn the home side to their fifth defeat in six games.
Taylor said: "It`s not a nice situation to be in but we have to stay determined to turn things around. The fans have been magnificent. I have no complaints about them. I can imagine them being extremely frustrated but we care as much as anybody. We appreciate the support we have had, home and away.
"Our first-half performance deserved more than one goal. We conceded a very poor goal just before half-time, giving Delroy Facey a free header because people got away from their markers. We are in this position because people are switching off and not fulfilling their jobs, which is disappointing.
"Lincoln took the game to us in the second half but we had some good chances. It was amazing that Dave Syers didn't hit the target from a few yards out, but the goal just before half-time was a killer for us.
"Ashley Grimes was allowed to travel too far with the ball in the build-up to their second goal and that, too, is disappointing."
Source: PA
Source: PA