Pompey still have a mathematical chance of reaching the League One play-offs with a couple of fixtures remaining.
But a 1-0 defeat to top six rivals Charlton at a packed Fratton Park means it is now a remote possibility.
They lie four points adrift of the final spot and the two teams directly above – Scunthorpe and Plymouth – both have games in hand.
Kenny Jackett will certainly not be giving up on the chase, although he has started to his cast his mind forward to the next campaign.
The Blues boss said: “It does look like it (missing out) might be the case, although we’ll have to see what happens in the last couple of games.
“But if we want to be successful next season – which we do – then we have to finish this one as well as we possibly can.
“There are certain things that we need to improve on – whether that’s power, experience, organisation or a little bit of all of them.
"If we want to be successful next season – which we do – then we have to finish this one as well as we possibly can."
“A number of younger players have had their debut season and improved, but they have to be hungry enough to step on again.
“Recruitment will also be key over the summer because we need to keep our good players and add more of them.”
Jackett conceded that their opponents were superior in the centre of the park, with Nicky Ajose’s strike late in the first half enough to secure victory for the Addicks.
He said: “Charlton won the midfield right the way through the game and we really didn’t crack that area, perhaps missing the power of Anton Walkes.
“Ajose broke out into space – as he did on a few occasions – and it proved to be the decisive moment of the game.
“Our crowd were fantastic to really drive the players on through the second half and we created a lot of pressure.
“Their keeper made a couple of good saves – one from Connor Ronan and then a deflected Brett Pitman free-kick that he did very well to keep out.
“We built some momentum going towards the end housing our own fans, but just couldn’t find that bit of spark.”
Pompey were dealt a defensive blow at the break, with Nathan Thompson and Jack Whatmough both unable to return to the pitch.
Jackett explained: “Nathan has quite a bad dead leg, while Jack pulled his groin, which limited the substitutions we were able to make.”