As the scoreline suggested, it was a good performance from the home side, but not a flawless one.
They edged a first half where the visitors posed problems on the counter-attack, and having stretched their interval lead from 2-1 to 4-1, ought to have won by a bigger margin.
Moore is looking forward to putting some of those things right on the training ground this week.
“We've got to keep going, we need to get better,” he demanded. “There are lots of things as a manager I can highlight on the video to the team next week and structure the training to really look at those areas..
“I'm grateful it's one game a week at the minute because it's going to ramp up and I'm just trying to take advantage of that.
“I thought it was a frantic game at times, end to end but when the chances came, we took our chances and got three valuable points.
“It was a bitty game in spells but I thought we settled down more second half and started getting some of the patterns going.
“Credit to Bristol Rovers, they made it difficult for us, they changed their shape and system for the first time this season and we had to fight hard for it.
“We created lots of chances and might have got a few more.
“At half-time we said our work off the ball had to be more solid but we thought if we could show a little bit more composure on the ball we'd get chances and be able to work in behind their defensive unit.
“Some of our football around their area was really good and some of our composure at times was good. Some of our play was erratic and messy at times but it's the third game in (to the season) and we've got another week to work at it.”
Goalscorer Jon Taylor, Reece James and Fejiri Okenabirhie all missed good chances for a fifth, and Tyreece John-Jules was indecisive when played through at the end of a fine individual performance.
“One of the messages to the players was we could have been a bit more ruthless when we got in the opposition area,” said Moore.
“Again it's something to look at but I was pleased with the three points. We had to stay at it and we did.”
One player who cannot be criticised for his goal output is midfielder Madger Gomes, who scored his fourth goal already this season, having not found the net previously for Doncaster. A later miss by him could therefore be excused.
“Madger is in a real rich vein of form in terms of scoring goals. He's getting in the box more and he strikes a clean ball,” said his manager.
“He probably feels he could have got another goal when the ball came across and he didn't quite sort his feet out.
“It's good to have goalscorers and threats from other parts of the team.”
The quality of Doncaster's football at times was very good, led by Arsenal loanee John-Jules at centre-forward, and Brighton and Hove Albion loanee Taylor Richards playing in the hole behind. Richards was another to find the net.
“It was a lovely right-foot finish, change of feet,” said Moore. “He's got wonderful balance, cleverness, creativeness, beautiful feet, he's strong and he moves well with the ball.
“The nearer you get him to the opposition goal, the more you see of him.”
Winger Jason Lokilo, who had a good first half, failed to reappear for the second half, but Moore said it was not a major concern.
“Jason came off more with fatigue,” he revealed. “He's had a good start and we've had a real, tough gruelling training session this week so we pulled him off as a precaution.”
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