A fine goal from Adam Phillips proved the difference, with wins for Oxford and Charlton ensuring the Blues finished in eighth position.
They improved following a poor opening 45 minutes, but Stanley held on to end the promotion dreams of the Fratton faithful.
Danny Cowley made a single change from the side that beat AFC Wimbledon at Plough Lane the previous week.
Jack Whatmough returned from a four-match ban to replace Sean Raggett at the heart of defence, with Paul Downing keeping his spot in the side.
A fit-again Jordy Hiwula – who had been out for more than a month with an ankle problem – was named among the substitutes.
There was a minute’s silence before kick-off in memory of club legend Alan McLoughlin, who sadly passed away earlier in the week at the age of just 54.
It was Pompey who threatened first, but Toby Savin denied John Marquis when the striker collected Ronan Curtis’ threaded pass.
But Accrington were playing with a freedom that their position in the middle of the League One table afforded.
They began to take control of the contest and stopped their opponents finding any kind of rhythm going forward.
And Stanley deservedly broke the deadlock midway through the first half, with Colby Bishop and Harvey Rodgers working the ball across to Phillips, who lashed a shot into the roof of the net.
The same player almost doubled their lead soon after, but Craig MacGillivray got down to his right to push behind a low 35-yard free-kick.
Set-pieces were causing plenty of problems in the Blues back-line, with a succession of corners sent into the mixer.
Pompey might have levelled in stoppage-time, only for a teasing Curtis delivery to somehow evade everyone as it flashed just past the post.
There was still time for Accrington to find the net again, when Bishop nodded home a Sean McConville free-kick, but the striker had his celebrations cut shot by an offside flag.
Accrington Stanley 1
The hosts came out with plenty of energy following the interval and suddenly space opened up for Curtis.
He advanced almost half the length of the pitch before hitting a long-range effort that Savin managed to turn behind.
The same player was then unable to keep a shot down after the ball had run into his path when Marcus Harness’ attempt was blocked.
And more good work from Curtis fashioned another opening, with the winger cutting in from the left and finding Marquis, but Savin was quickly off his line to make the save.
Cowley made a triple substitution just before the hour mark, with Hiwula, George Byers and Harvey White on for Downing, Ben Close and former Stanley full-back Callum Johnson.
Skipper Tom Naylor dropped into a back three with Whatmough and Lee Brown, as Pompey went on the attack.
And Byers soon showed some nifty footwork to make himself some space to shoot, but Savin was equal to the effort.
The Blues were playing with plenty of urgency, although their visitors were defending resolutely to keep them at bay.
Charlie Daniels was thrown on for Ryan Williams for the closing stages and a low centre was cleared after he collected the ball from Curtis on the overlap.
And the defender was then played through on goal by Harness, only for Savin to tear from his line and make a fine save.
It looked like Daniels was fouled by Ben Barclay as he tried to get his shot away, but referee Sam Purkiss waved aside the appeals.
Curtis looked like he would get a late leveller when he sent a free-kick through the wall, only for Savin to again come to the visitors’ rescue.
And time ultimately ran out on Pompey, who will now prepare for a fifth successive season in League One.
Pompey (4-2-3-1): MacGillivray; Johnson (White 59), Downing (Hiwula 59), Whatmough, Brown; Naylor (c), Close (Byers 59); Harness, Williams (Daniels 79), Curtis; Marquis
Booked: Harness, Downing, Byers, White
Subs not used: Ward, Raggett, Cannon
Accrington (3-4-1-2): Savin; Barclay, Nottingham, Burgess; Rodgers, Phillips, Morgan, McConville (c); Russell (Scully 65); Bishop, Charles
Goals: Phillips 23
Subs not used: Buckley, Perritt, Sama, Martin, Mansell, Smyth
Referee: Sam Purkiss