The Blues sold out their away allocation of 616 tickets for Monday night’s trip first-round tie against the National League side – despite the clash taking place in front of the BT Sport cameras.
It meant many fans had to book days off work to travel to Wetherby Road, as well as getting home in the early hours of Tuesday morning.
And to make matters worse, kick-off was delayed by almost an hour because of a power cut.
That meant the turnstiles were closed for a short while and supporters had to wait outside in wet and windy conditions until entry was granted.
Those difficulties were made worthwhile, though, as the travelling Fratton faithful eventually made the trip back to the south coast happy following a 2-1 victory.
It was backing Haunstrup fully appreciated – and the full-back heaped praise on everyone who made the journey to north Yorkshire.
The defender said: ‘It was great to get through to the next round, especially for the fans.
‘We went up on the plane in the morning and it was a long day for us.
‘A lot of the fans probably took a day off work and it deserves a massive, massive well done to them and we're happy to just get them a result.
‘It wasn’t the best game, we didn’t particularly play well, but we got the result and are into the next round.
‘The fans had to wait outside before the stadium opened and they won't have got home until late.
‘That’s why the fans deserve massive respect as always.’
It proved an even longer day than Pompey expected with the game being pushed back by 55 minutes.
Power failures put the game at risk before it eventually got under way at 8.40pm.
But Haunstrup was glad the clash against the National League side did get the go-ahead, rather than be postponed to another date.
The academy graduate added: ‘It was a really long day for us.
‘We just wanted the game on more than anything and obviously it wasn’t ideal.
‘The main focus is the league and climbing up the table, which we’re doing now.
‘We didn't want to come back up and have to cancel a league game so it was good to get it played.’