David Hopkin rued Bradford’s composure in the final third as Pompey piled more misery on his team.
The Blues’ 1-0 victory condemned the basement side to a seventh straight defeat.
Gareth Evans’ 12th-minute strike against his former club settled the clash, with Kenny Jackett’s men extending their advantage at the summit of the League One table to three points.
Bradford didn’t look like a side rooted to the bottom of the division, though, and could have snatched at least a point.
They had a number of opportunities to equalise – the best being Hope Akpan’s in stoppage-time but he sent his shot over the crossbar.
Hopkin took solace from Bradford’s performance against the table-toppers.
But the boss felt his troops should have been more clinical.
He told the Bradford Telegraph: ‘Portsmouth had one chance in the first half and one in the second. I think we’ve had five or six good chances.
‘We’ve had three free headers from set-plays, we’ve had Hope Akpan’s at the end, David Ball’s free-kick and balls slashing across the six-yard box that just need a touch.
‘The application was great and there were a lot of positives to take from the game.
‘Even when we went 1-0 down, we didn’t crumble. But it’s a hard one to take.
‘You’ve got to give them credit because they’ve hung on. But we have to do better with the chances that we did have.’
The Bantams had Adam Chicksen dismissed in the 83rd minute.
The left-back picked up a second booking for a foul on Jamal Lowe.
Hopkin believes Chicksen’s dismissal was harsh, however.
He added: ‘I think it was harsh. You trip somebody and they’re just a wee bit quicker than you.
‘You go to ground and you always give the referee an option.
‘He’s devastated but I thought he played really well after not doing anything for 10 weeks.’
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