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.
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."
Cheltenham manager Mark Yates admits felt his Robins earned their point as they withstood a late Pompey assault.
He said: "I thought we were excellent in the first half. It was probably a nine-out-of-10 first half. We were just missing a goal.
"We passed the ball really well and were competitive. We looked organised and we looked dangerous. We just didn't get the goal we probably deserved.
"In the second half, we had to withstand it. We weren't quite as good - probably a seven out of 10. But every point is valuable in this league at the moment. It's so tight. It was important we didn't come here and get beaten. We can be reasonably pleased with our efforts.
"We talked about dealing with the crowd and we kept them really quiet for 70 minutes because of the way we were playing. Bar one scramble at the end, I thought we were pretty comfortable.
"We passed the ball really well, but lacked the killer touch. I think they could say that as well and a draw was a fair result. In the first half we edged it. In the second, they edged it towards the end."
- Sports & Recreation