Sean Raggett insists that Pompey will keep battling away until the end of the season.
A 1-0 reverse at Plymouth ended an impressive eight-match unbeaten run and dented hopes of making the play-offs.
It leaves the Blues sitting eight points adrift of sixth spot in League One with just nine fixtures remaining.
But Raggett has promised that nobody will give up on the chase while there is still a chance to extend the campaign.
The defender said: “We’re pretty gutted with that result because we thought that, on the whole, we had played well.
“We know the situation that we’re in and that we need to win as many games as we possibly can now.
"Of course we’re the outsiders now, but while there’s still a chance, you have to keep believing and give everything."
“The guys have still got aspirations of making the play-offs, even if some people might think that’s ridiculous.
“But this group will keep on fighting right until the end and that’s why we’re all so frustrated that we couldn’t get over the line at Plymouth.
“Of course we’re the outsiders now, but while there’s still a chance, you have to keep believing and give everything.”
Ryan Hardie netted the only goal of the game, converting a Panutche Camara pass after Louis Thompson had been dispossessed by Jordan Houghton.
Raggett said: “There was an unfortunate mistake for their goal and he has been one of our best players this season.
“So we needed to dig Louis out from that moment, but we just didn’t have enough at the end to get the ball in the net.
“I don’t think we really tested their keeper. We got into good areas and were then lacking with our final action.”