The first half in particular was one-way traffic, but the Dons failed to take advantage of their superiority and eventually paid for it as Ryan Lowe's 90th-minute goal snatched the points for Tranmere.
Victory for Rovers lifts them five points clear of relegation zone, but this was a third game without a goal for the home side.
In a first half the Dons controlled, Ben Reeves was denied twice by Tranmere keeper Owain Fon Williams, while Powell lifted a great chance over.
They were hit with a sucker-punch at the death as Jake Cassidy got in behind down the left and cut the ball back for Lowe to tap into an empty net.
Moore said: "We don't get too much here and staying in the game was the big thing.
"We weren't brilliant first half where they were the better side I thought.
"We had a talk at half-time where we told them to be more adventurous and show a bit more belief that we can win the game, which I always thought we could.
"When they're playing a man in the hole we couldn't be as deep as we were in the first half because we caused our own problems so we needed to push up.
"Once we did that it condensed the areas, there was no where for them to go and they had to hit long balls and those long balls suited us.
"In the end we had Steve Jennings, who is our deep-lying midfielder, on the edge of their box to make the goal - it shows how much better we played second half."
- Sports & Recreation
- Owain Fon Williams