The Blues were condemned to a 4-0 loss against Southampton in the third round of the Carabao Cup at Fratton Park.
However, it was Kenny Jackett’s men who were on top during the opening exchanges, with John Marquis hitting the post and Brett Pitman having two efforts saved.
Pompey were punished twice by Danny Ings, though, before half-time, while Cedric and Nathan Redmond compounded more misery on the hosts after the break.
The Blues have also been in poor form in League One, winning just one of their opening seven fixtures and sit 20th in the table.
But despite being put to the sword by their bitter rivals, Haunstrup took heart from Pompey’s overall display.
He said: ‘It’s probably the best we have played all season.
‘In the first 15-20 minutes, we gave them a real match.
‘Against a Premier League team in Southampton, you need to take your chances.
‘If you don’t then eventually, Redmond comes on and he puts and end to it.
‘We came in at half-time, played well and kept going in the second half.
‘But once the third and fourth went in then it’s hard to get going.’