Bradford had made a good start to the New Year with two wins in three days against Lincoln and Bury, but they were brought down to earth by Barnet, who had lost five of their previous six matches.
The visitors turned the match on its head by scoring three times in a six-minute spell during the second half after City had taken a fortunate half-time lead in stoppage time.
Defeat was a bitter pill for Bradford supporters to swallow after they had seen their side turn on arguably their best performance of the season in the 1-0 win against Bury and Taylor said: "It was very frustrating. We have got be better than that and we have got to learn from it.
"I don't expect us to play well every time, but I expect us to defend better at throw-ins and corners. The first two goals Barnet scored I don't think they could believe how easy it was, but their third goal came from good counter attacking."
Defender Luke Oliver scored City's goal heading home David Syers's cross after the midfield player had managed to kick the ball away from debutant England Under-19 goalkeeper Liam O'Brien's grasp.
The match turned when the visitors scored a bizarre equaliser after 61 minutes, substitute defender Rob Kiernan inexplicably heading into his own net as he tried to deal with Glen Southam's cross.
Three minutes later defender Anwar Uddin put the visitors in front with a far-post header from Mark Marshall's corner and they added a third three minutes after that through Ricky Holmes after Izale McLeod had broken away down the middle.
Bradford City: Pidgeley, Eckersley, Duff (Kiernan 50), Oliver, Luke O'Brien, Adeyomi (Cullen 45), Syers, Bullock, Daley, Hanson, Evans. Unused substitutes: McLaughlin, Doherty, Osborne, Chilaka, Threlfall.
Barnet: Liam O'Brien, Francomb (Kamdjo 85), Devera, Uddin, Parkes, Jarvis, Southam, Hughes, Holmes (Vilhete 90), Marshall, McLeod. Unused substitutes: Cole, Stimson, Cox, Kelly, Taylor.
Referee: D Foster (Newcastle-on-Tyne).
Man of the match: Luke O'Brien.
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