The Blues were held to their third straight goalless draw with striker Patrick Agyemang closest to netting when he scuffed a shot against the foot of the Brewers post after wriggling free in the box in the 51st minute.
Barker questioned his team's desire to deliver the goals and admits his players are fighting for their Fratton Park futures as he ponders a major off-season overhaul in a bid to spark a promotion charge next term.
He said: "I'm not going to get promoted with this group. We have 13 players out of contract this summer; all of whom are fighting to earn the right to continue playing at this football club. Every day and every time they go out there is a job interview, if you like.
"I've watched every goal in League Two for the last few weeks and I see people individually creating chances, creating goals and scoring goals. I don't see that here.
"I'm still working out where we're going to go next year in terms of how we're going to get promoted. I'm finding out a lot about players on a daily basis - some good and some bad. I think there is a long way to go and a lot of changes that need to be made."
Pompey's scoring frailties continue to grate with Barker as they have managed just five in their last nine games.
He said: "I don't think there's a lack of chances. I just don't think we've got anybody who has the desire to go and score the goals. People thought goal scoring wasn't an issue when I first came in - it is."