RORY McArdle held his hand up after City's agony at Wembley for missing one of their best scoring chances.
The centre half had netted with headers in each of his previous two appearances in play-off finals.
Yet he blew a gilt-edged opportunity in the second half against Millwall when he nodded over from close range.
McArdle said: "I should have done better with my header, to be honest. I was six yards out and in the middle of the goal.
"I actually thought I was offside but I tried to keep it down. It just wasn't to be."
City's ploy to switch to three centre halves shackled Millwall's dangerous front duo Steve Morison and Lee Gregory – until five minutes from time.
Then both combined for Morison to jab home the goal that sent the Lions up to the Championship.
"Conceding a goal that late on left ourselves with very little time to get back into the game," said McArdle.
"Gregory got a little nick on the cross and then it fell to Morison and that kind of luck didn't really go for us.
"We had some good chances during the match and, even at 1-0, a few balls went into the box that might have fallen to someone on another day.
"Our set-pieces were also good but we just needed that bit more fortune and quality in the final third, which let us down a bit.
"But the lads deserve a lot of credit for keeping going because, when you concede that late on, it would perhaps be easier to think that's us done."
McArdle is among the group of players whose City's future is now up in the air. His contract is up and talks are expected to take place with the club this week.
The 30-year-old defender, who played his 231st Bantams game on Saturday, revealed it was a quiet dressing room afterwards.
But he felt they still deserved plaudits for reaching Wembley following all the ins and outs of last summer.
He said: "It's still been a massive achievement to get here. It would have been great to go one step further but, if you look at the changes made at the start of the season in the ownership, management and playing staff, it was always going to be a hard start for us.
"The gaffer (Stuart McCall) had to build a new squad but we're still disappointed not to finish the job off. He didn't say too many words and I don't think it would have really helped anybody anyway.
"He'll probably let the dust settle first before we talk about the match. Losing was as tough as it comes really and we're all gutted."
City's beaten players also had to face the sight of taunting Millwall fans confronting them on the pitch.
McArdle said: "It was horrible to experience that so close up."
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