There were no goals after 90 uninspiring minutes, but the Bantams got the better of their League One opponents 3-2 from 12 yards.
The decisive moment came when Pools' Evan Horwood's kick cannoned off goalkeeper Jon McLaughlin, hit the bar, bounced on the line and rolled to safety.
"It was a decent performance in parts, not as good as the last two, but yet again we lost," moaned Cooper. "On penalties this time and we hit the post three times in the shoot-out.
"We had chances, they did too and they are a decent side. When we started moving the ball quicker we did better. Yet again the young lads were excellent out there.
"The back four were good, kept a clean sheet which is positive. The last penalty hit the keeper, hit the bar, hit the line and stayed out. When things are hard, and they are just now, it goes against you. I thought my luck was back in when they missed their first penalty - and then it ends up against us."