In many ways it was a classic FA Cup tie.
Luton were protecting a slender lead against their higher-ranked opponents, while Pompey poured forward and rained shots on goal.
But taking part in a vibrant encounter will be of little consolation to Kenny Jackett following a first round exit.
James Collins scored the only goal on the stroke of half-time to ensure it was the League Two side who progressed at Kenilworth Road.
It was a fourth successive defeat for the visitors and Jackett knows they have to turn their form around.
The Blues boss said: “We’re in a poor run at the moment. We have to stick together and work hard to keep the players’ confidence high.
“It was a really close game, but the first goal is a key one and they managed to find one out of nothing.
"We can’t talk about luck – we have to make our own luck."
“It was an end-to-end affair and we looked pretty comfortable defensively aside from their goal.
“We found some momentum in the second half, although ultimately couldn’t find a way back into the tie.
“We can’t talk about luck – we have to make our own luck. We’re out of the FA Cup, which is a competition I value, but it’s not to be.
“So we’ll keep reinforcing the good things that the players do because we had a lot of possession in and around their box.”
Pompey will now have two key players suspended for their League One trip to Blackpool next Saturday.
Nathan Thompson was sent off late in the game, while Stuart O’Keefe also has to serve a one-match ban after collecting his fifth yellow card of the campaign.
Jackett said: “It was a bad decision by Nathan for the second booking and it didn’t help us. It was difficult for us after that.
“Of course it’s disappointing, but other players will come in and it’s up to them to work hard and try to keep the shirt.”