Victory lifted Dale to the top of League Two, but it was a far from routine win for the home side.
They were behind just 40 seconds into the game when Luke Norris smashed home a glorious 25-yard strike.
George Donnelly then netted the winner two minutes later to make it five successive wins on home turf.
"We have a very deflated dressing room after that," said Boothroyd. "It's all about very fine margins between winning and losing and for long periods you wouldn't have known which side was at the top of the league.
"But I said to the lads afterwards that the reason they are top of the league is because they keep going to the very end and we make silly mistakes.
"We conceded a silly free kick, they score and the whole crowd is lifted and they get the momentum. The third goal was a poor one from our point of view.
"The game looked finished at 2-1 and it's difficult to take a defeat like that. But they are on a great run at the minute and things are going for them.
"We have to keep calm, show bloody-mindedness and keep going because I know that we will start winning games. There were many encouraging signs but they are difficult to see at the minute because we have lost."