A Sam Sodje own goal gave Tranmere hope from 2-0 down, but they were unable to stop their hosts recording a 10th straight home win.
The Wirral club still occupy the final play-off spot in League One, though, but Scunthorpe are just two points behind them and have two games in hand.
"With two games left we still have a chance of making the play-offs, though this makes it more difficult," admitted Moore.
"When you come to Leeds you have to defend well and unfortunately we didn't. We had a real go and didn't sit back. On another day we would have taken something from the game.
"At 2-1 we still had a chance but their keeper made a save from Anthony Kay that I don't think he knew much about, and they punished us as at a set play. We played well but we didn't take our chances and they did."