They fell behind to Sean McConville’s strike just after the break, but Ben Close’s ninth goal of the season drew them level.
Close also hit the woodwork as the Blues chased a winner, with the dropped points allowing Charlton to climb above them into third spot.
Kenny Jackett made five changes to the side that were narrowly beaten by Peterborough earlier in the week.
Gareth Evans returned to skipper the team, while there were also starts for Oli Hawkins, Viv Solomon-Otabor, Bryn Morris and Anton Walkes.
Brett Pitman, James Vaughan, Ronan Curtis and Nathan Thompson all dropped to the bench, with Jamal Lowe missing out completely.
With it being the final game of the regular campaign, there were plenty of awards given out prior to kick-off.
They all went to Matt Clarke, who collected the main The News/Sports Mail Player of the Season prize, as well as trophies from 12 supporter groups.
The fans then fell silent as the names of all those fans – and former players – who have passed away over the course of the campaign were read out.
When the action got underway, there was a rather pedestrian pace to proceedings and a flat atmosphere to accompany it.
Accrington almost livened things up with an early goal, as McConville met Janoi Donacien’s cross with a header that bounced back off the bar.
Solomon-Otabor had an effort blocked at the other end, with a long-range Close strike comfortably dealt with by Dimitar Evtimov between the Stanley sticks.
Pompey really should have been awarded a penalty on 18 minutes, with Donacien clearly tugging at Hawkins’ shirt, but referee Scott Duncan appeared not to notice.
It certainly did not feel like the end of the campaign, with an unseasonable chill in the air causing coats to be put back on.
There were not an abundance of clear-cut opportunities on the pitch, although an angled drive from Paul Smyth was saved by Craig MacGillivray.
Pompey then had a great chance when Evans’ free-kick found Christian Burgess in the box, but the defender did not get enough on his header and the ball flew past the post.
Hawkins and Morris also sent efforts over the crossbar just before the break, as the hosts tried to find a breakthrough.
Accrington Stanley 0
Morris did not emerge following the interval, with Curtis brought on and Evans moving to a more central role.
There were just 44 seconds on the clock when Accrington opened the scoring, courtesy of McConville’s fine low strike from the edge of the box.
Pompey looked to hit back immediately and Curtis’ teasing delivery took a slight deflection to prevent Hawkins from tapping in from close range.
There was another opportunity for Burgess, with the defender heading wide after rising to meet a cross from Evans.
But it was CLOSE who levelled just before the hour mark, swapping passes with Hawkins and surging forward before beating Evtimov with a low finish at the keeper’s near post.
Hawkins was immediately brought off, with a fit-again Omar Bogle coming on to lead the Blues’ forward line.
Pompey were trying to find a winner and an acrobatic Bogle effort went past the post, while a clearance hit Pitman and flew off target just moments after the skipper had replaced Evans.
It was certainly a busy introduction for the striker, who scuffed wide after Bogle’s pass had gone just behind him.
But it was Close who almost gave the hosts the lead with a superb shot from outside the box that thundered against the angle of bar and post.
Pompey were pouring forward in search of a winner, while Accrington looked to exploit that on the break.
But despite a frantic conclusion to the action, neither keeper was really tested as the teams had to settle for a point each.
Pompey (4-2-3-1): MacGillivray; Walkes, Burgess, Clarke, Brown; Naylor, Close; Evans (c) (Pitman 74), Morris (Curtis 46), Solomon-Otabor; Hawkins (Bogle 60)
Goals: Close 59
Subs not used: Bass, Thompson, Haunstrup, Vaughan
Accrington (4-4-2): Evtimov; Donacien, Sykes, Hughes, Richards-Everton; Clark (Sousa 66), Barlaser, Conneely (c), McConville; Armstrong, Smyth
Goals: McConville 46
Subs not used: Warner, Rodgers, Ogle, Brown, Simmons, Zanzala
Referee: Scott Duncan
Attendance: 18,439 (241 away fans)