Mark Hughes admitted the Bantams lacked composure and professionalism as a last-minute goal condemned his side to their first defeat of the season at Barrow.
Second-half substitutes Jake Young and Andy Cook equalised twice before Josh Gordon’s stoppage-time finish.
Hughes believed there was “no excuse” to lose the encounter, particularly after a positive first-half showing.
He said: “I was reasonably happy with the first half. I thought we had a lot of control.
“With the second half, I was really disappointed with what we produced. We maybe had a bit of tiredness, and did not really concentrate. This always happens with emotions at the end of the game.
“It should not be an excuse. There are a lot of guys here who have faced situations like that and dealt with them. Unfortunately, we did not do that today, which is a real shame.
“Credit to Barrow. They had a lot of energy up front. They were chasing lost causes and we did not deal with the long ball or anything that dropped down. They were the first to get on to it, and we have got to get better.”
Hughes was pleased with the impact his substitutes had in the second half, as City scored their first goal of the campaign through new signing Jake Young, but believes the Bantams have work to do in order to get their first three points.
He added: “Andy Cook and Jake Young did really well when they came on. They really affected the game, which was what we needed.
“Jake was a real threat when he came on. He scored a great goal, and we see that every day in training.
“We needed to have that composure when we got it back to 2-2. It should have been game over.”