The Robins edged the first half, which saw Jermaine McGlashan denied by a superb save from Pompey keeper Trevor Carson after 20 minutes. This was before Ashley Vincent fired against the post from 20 yards when the ball broke from the resulting corner.
Pompey should have won the game through Jake Jervis, when Ricky Holmes put him clean through on goal after 14 minutes, but the Blues hitman blazed wastefully wide of the target.
Despite keeping their fourth clean sheet in five matches, Pompey have scored just three times in those games.
While Barker was buoyed by another Pompey shutout, he admits his men must pose more of an attacking threat.
He said: "The touch and decision-making in terms of that final pass and when to get a shot off just let us down. I don't think we worked their goalkeeper enough and obviously that starts with the strikers.
"I felt it was important to go positive. We went positive at home with two strikers and two wide players. We threw everything that we could at them and tried to be positive.
"There are positives we can take from it - another clean sheet and the fact we have lost just five games in the last 16.
"We've become harder to beat. But we now need to turn that around and win the games."