The Bantams were leading at half-time thanks to Luke Oliver's header in injury-time, but three goals in six minutes condemned them to defeat.
First, Rob Kiernan headed into his own net in the 61st minute, Anwar Uddin nodded in three minutes later and Ricky Holmes wrapped up the win after 67 minutes with a tap-in.
Taylor said: "I think we can play a lot better than that. I wasn't very pleased with the way we played in the first half and we didn't deserve to be 1-0 up at half-time, but we started the second half well and if we had scored a second goal then I think it would have been a different afternoon.
"We don't expect to play well every time, but I do expect us to defend better at a throw-in and a corner which led to Barnet's first two goals than we did.
"The first two goals Barnet scored I don't think they could believe how easy it was, but their third goal was the result of very good counter-attacking - that was good play."