Arsene Wenger insisted Arsenal's players should not feel embarrassed about crashing out of the Capital One Cup - despite losing to a side 64 places below them in the league.
Bradford won 3-2 on penalties after the match ended in a 1-1 draw after extra time at their Valley Parade ground.
Just one player in Phil Parkinson's side commanded a transfer fee - £7,500 (Dh44,400) for James Hanson - compared to Wenger's multimillion pound English Premier League side.
The defeat will only strengthen the pressure on Wenger, but the Arsenal manager insisted he was disappointed rather than embarrassed by the result.
"You feel embarrassed when you don't give everything but I feel the team did fight and they will be more disappointed and frustrated," he said afterwards.
"It's disappointing but congratulations to Bradford. They defended well, started stronger than us and in the second half and extra time it was all us but we couldn't convert our chances.
"It was a typical English cup game on a difficult pitch and overall we lost on penalties but I cannot fault the efforts, we kept going until the last minute and in the end Bradford got on top of us.
"Of course we missed three penalties and that's a lot to take."
Arsenal did not force a save out of Bradford keeper Matt Duke until the 69th minute, but Wenger insisted his team had created enough overall.
He added: "They defended very well, very deep in their own half, the pitch was a bit slippery and there was no space.
"We played with a very offensive team and for over an hour played with five strikers but couldn't score.
"Where does it leave our season? To focus on the next game, sport is about that."
Bradford took the lead in the 16th minute after Garry Thompson volleyed home Will Atkinson's free kick, and could have made it two moments later until Kieran Gibbs' goalmouth clearance.
Inspired goalkeeping from Duke kept Arsenal at bay until three minutes from time, when Santi Cazorla whipped in a cross for Thomas Vermaelen to head home.
Arsenal continued to press during extra time, with Cazorla striking the crossbar from 30 yards out, but Bradford held out for penalties.
The English Premier League side were always on the back foot from when Cazorla had their first spot-kick saved, even more so when Marouane Chamakh hit the post.
Bradford could even afford to see Wojciech Szczesny deny Ritchie Jones and Stephen Darby before Vermaelen's miss sent Valley Parade into ecstasy.
Bradford boss Phil Parkinson said his players - who won their ninth successive shoot-out - should be given credit for outperforming a full-strength Arsenal side.
He said: "I don't think the enormity of our achievement has quite sunk in. When get up tomorrow morning and see the headlines in the newspapers they will realise what they have done.
"There is a big gulf between the two teams in terms of finances and places in the divisions.
"I don't want the talk to be about the penalties, I want it to be about the performance. Arsenal have played their best team tonight and we were three minutes away from beating them, then we have had the setback of conceding a goal and had to dig deep again in extra time.
"I hope this can be the first of many nights like this for Bradford City. We want to put Bradford on the map again. I want them to have a team to be proud of."
Elsewhere in the cup, Andreas Weimann struck twice as Aston Villa came from behind to beat Norwich 4-1 win at Norwich.
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