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.
Yates 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."