The recently-appointed Pompey boss, having suffered a second successive loss since taking charge, questioned the mindset of the players he has inherited and whether they deserved to be donning the shirt of such a big club.
More than 1,300 travelling fans witnessed another poor performance and Barker was not about to offer any excuses.
"It can't be coincidence that over the last eight or nine weeks there have been no wins and it's the same players involved, even if there is a different manager," he said.
"If you can't change the mindset of people perhaps you have to change the people and we will have to look at that during the January transfer window.
"We have a fantastic football club with wonderful support. Unfortunately, I'm not sure the players realise how lucky they are to be playing for such a good club
"I thought we were the better team in the first half, but games last 90 minutes and Bristol were probably good enough in the second half to deserve to win the game."
Ollie Clarke broke the deadlock five minutes before the break, rifling home a low right-footed half-volley from the edge of the box after being teed up by Eliot Richards. It was his first goal for Rovers and a sweet moment for a youngster who has had to overcome serious knee and hamstring problems.
David Clarkson doubled the lead after 77 minutes, lashing home a right-footed shot from an angle when Oliver Norburn's pass put him through.
The impressive Clarkson had earlier struck the Portsmouth crossbar with a fierce 15th-minute shot from the corner of the penalty area and the home side were well worth the three points.
Ryan Bird squandered Pompey's best chance, shooting tamely at goalkeeper Steve Mildenhall from 12 yards after 26 minutes.
And it took a stunning second-half save from Trevor Carson to keep out a Clarkson free-kick bound for the top corner and prevent Rovers winning by a bigger margin.
Pirates boss John Ward was delighted by a rousing display which sent Rovers fans home full of festive spirit towards the end of a tough year.
He said: "It was a really good team performance and it would be wrong to single out players because they all did well.
"We are all thrilled for Ollie Clarke because he has had to overcome some serious injuries for such a young player and this was his reward for a lot of hard work.
"You could tell by the way the other lads mobbed him how pleased they were for him. Although his job is to protect the back four, I have been encouraging him to get forward into shooting positions.
"The fitness of our team showed after slogging through the downpour in the abandoned cup tie at Crawley in midweek and I couldn't be happier.
"If you count that game we have only lost two of our last 12 matches and that is something to build on."