At least at Spotland they can be partly comforted by a much-improved second-half showing when they were banging on the door.
John Marquis, in particular, had two glorious chances after the break, while Rochdale defended with resilience and bravery to survive under pressure.
Nonetheless, Kenny Jackett’s side were not potent enough in attacking to overcome their hosts.
Had it not been for Jack Whatmough’s goal-line clearance and a superb save from Craig MacGillivray, both in the final five minutes, there could have even been defeat.
As it was, Pompey can reflect on another deeply disappointing outcome, repeating last weekend’s goalless draw against Shrewsbury.
Michael Jacobs was given 24 minutes off the bench for his debut, a player it is hoped will have a talismanic impact on this frustrating Blues side.
There were flashes from the former Wigan man, yet the visitors couldn’t capitalise on their encouraging second-half pressure - and that remains the concern among the Fratton faithful.
Shrewsbury and Rochdale will, in all fairness, not be promotion contenders, yet Jackett’s men have failed to claim victory over either.
And with the manager coming under increasing fire from supporters held at a distance by behind-closed-doors fixtures, once again they have seen little to persuade them to stand down.
There were three changes to the side which suffered a 4-0 Carabao Cup exit at Brighton on Thursday night.
With Callum Johnson back from being cup tied for Brighton, he replaced James Bolton at right-back.
Bolton was not included in the match-day squad, although carried out fitness work on the Spotland pitch before kick-off.
Elsewhere, vice-captain Lee Brown returned for Cam Pring at left-back, with the loanee among the substitutes.
Finally, Andy Cannon came in for Ryan Williams against his former club, operating as the furthest forward of his central midfielders.
Gareth Evans was not included in the squad, although Jacobs was among the substitutes for his first involvement since joining almost a week ago.
Meanwhile, Jack Whatmough was fine to retain his place after worryingly being taken off against Brighton following a knock to his right knee.
At the time, Jackett insisted the substitution was a precaution, and it turned out to be the case, with the defender able to feature against Rochdale.
Alex Bass was once more absent with his ankle problem, so Duncan Turnbull continued to offer a bench back up to Craig MacGillivray.
Once the match kicked off, Ryan McLaughlin had to receive treatment after going down under a challenge from Ronan Curtis.
It appeared theatrical, with no suggestion of a foul, the right-back then calling for medical attention, prompting a team-mate to put the ball out of play.
However, he was able to continue, without too much apparent discomfort.
A lovely move from the hosts on 12 minutes saw a fine spell of passing result in Jimmy Keohane clip a dangerous ball through which Craig MacGillivray managed to get to first.
At the other end, a jinking run into the box by Marcus Harness saw appeals for a penalty when his shot struck a Rochdale player.
From the loose ball, Johnson delivered a good cross from the right which was met with a far-post header from Curtis, which John Marquis just couldn’t get on the end of.
Ollie Rathbone was looking lively for the hosts and, on 16 minutes, lashed a shot from the edge of the area which flashed narrowly wide of MacGillivray’s right-hand post.
Pompey won their first corner on 24 minutes, which Curtis played short to Brown, whose cross from the left was just over the head of Tom Naylor.
Rochdale were looking the better side and on 27 minutes Aaron Morley clipped a ball into the box which was collected by Stephen Humphrys, who fired a shot over the bar.
Home keeper Gavin Bazunu was finally involved in the action on 28 minutes, when Tom Naylor’s drive from outside the box was fingertipped around the post for a corner.
The Blues suffered a scare when Bryn Morris attempted to lay the ball back, only to succeed in diverting it helpfully into the path of Alex Newby.
He burst down the right, drew MacGillivray, then fired a shot across the face of goal which went out for a throw-in.
On 35 minutes, Curtis brought the ball forward, and then took advantage of a fortuitous ricochet to shoot right footed, but disappointingly it was straight at the keeper.
Rochdale were forced into an early substitution, with the injured Humphrys replaced by Matt Done in the 38th minute.
The game was goalless at half-time and Jackett and Joe Gallen were deep in conversation when the teams re-emerged for the second half, no doubt plotting how to change things.
On 48 minutes, Cannon slipped the ball through to Brown on the overlap and the left-back’s cross to the far post was met with a Harness header which the keeper took high.
Moments later Pompey should have been in front when Bazunu shanked a clearance straight at Harness.
The winger in turn teed up Marquis for an opportunity, but instead the striker slid his shot wide of the far post from eight yards.
The striker knew he had wasted a golden chance and stood there contemplating afterwards.
The Blues appealed for a penalty on 58 minutes when Raggett appeared to be impeded as he attempted to meet an excellent Harness cross, but nothing was given.
The visitors were beginning to build pressure and firstly Cannon delayed shooting too long, then Johnson fizzed in a teasing cross which a Pompey body narrowly failed to get on the end of.
It was far better from Jackett’s men, who were looking the most likely side to net during an encouraging second half.
Jackett made his first change on 66 minutes, with Cannon replaced by Jacobs for his debut.
Pompey thought they had scored when Bazunu caught Brown’s right-wing corner and dropped it into his own net, but the referee ruled a foul.
Curtis made way on 79 minutes, with Ellis Harrison introduced alongside Marquis in a two-pronged attack.
Pompey pushed for the winner and another glorious chance fell to Marquis from Johnson’s header, but his attempt was pushed over.
From the resulting corner, Raggett’s smart shot on the turn was brilliantly saved by Bazunu.
With five minutes remaining, Harrison chased back to put in a tackle, only to succeed in putting Done through.
The Rochdale man initially missed his shot, then he watched Whatmough clear his second attempt off the line.
Pompey pushed for the winner, yet it didn’t come. And it’s another frustrating goalless draw.