Pompey suffered a first round Emirates FA Cup exit for a second successive season.
James Collins grabbed the only goal just before the interval to ensure it was Luton who booked their place in Monday evening’s draw.
But they were made to work hard for their victory at Kenilworth Road, with the Blues creating plenty of openings in the second half.
And Brandon Haunstrup does not believe that the result was a fair reflection of the visitors’ performance.
The defender said: “We wanted to progress, so of course it’s disappointing to go out in the first round.
“There were glimpses from us – especially in the second half – and we had enough chances to win comfortably.
"Their goal on the stroke of half-time was a real sucker punch."
“But when you’re on a losing run like we are at the moment, you just don’t seem to get that bit of luck on your side.
“Their keeper produced a number of vital saves to keep them in the lead and stop us getting at least a replay.
“Luton’s form this season shows that this will always be a tough place to come and unfortunately we weren’t able to get the result we wanted.
“Their goal on the stroke of half-time was a real sucker punch because we had defended really well and not given them any real opportunities.
“We came out after the break and created a lot of chances, though – on another day a few of them would have gone in.”
Haunstrup was making his first start since the start of September, with Dion Donohue preferred at left-back in recent weeks.
He said: “I just want to do the best I can, although I was blowing a bit towards the end of the game. The more you play, the fitter you feel.
“Starting a few matches earlier in the season was a real positive for me and I wanted to cement my place. So now I’m just looking to get my head down and work hard.”