Pompey kept a fourth successive clean sheet to continue their unbeaten start to the League One season.
But Danny Cowley was frustrated that his side were only able to leave Doncaster with a point to show for their efforts.
He admitted that they had to battle through a difficult period during the first half at the Keepmoat Stadium.
Cowley was much more impressed by Pompey’s display after the break, though, with Pontus Dahlberg the hero for the hosts with a penalty save from substitute Shaun Williams.
The Blues boss said: “We’re always disappointed not to win and felt we’d done enough, but unfortunately couldn’t take our chances.
“I thought we started well, but didn’t ask enough questions of our opponents when we had that control.
"Their goalkeeper has made two world class saves from open play and then also did well to keep out our penalty."
“Then we lost our way in the middle part of the first half and made technical errors, giving the ball away cheaply at times.
“We weren’t working hard enough to make the angles that would make space for each other. When that happens, it hurts our gameplan of pressing with intensity.
“But we got through that and came out in the second half with renewed energy, showing much more purpose.
“Their goalkeeper has made two world class saves from open play and then also did well to keep out our penalty.
“It’s the second one we’ve missed since we came here, but I thought that Willo and the rest of the subs did well when they came on.”
Pompey were without Marcus Harness, who was substituted at half-time of Tuesday’s win over Shrewsbury.
Cowley said: “We missed him. He’s got a little nick on his outside quadricep and it’s very low level, so we’re hopeful he’s back for Saturday.”