Danny Cashman put the visitors ahead five minutes into the second half after Kellan Gordon was robbed of the ball by Matty Dunn.
But supersub Danny Johnson levelled late for Stags just three minutes after entering the pitch.
“I wish we had got a point in our last four games,” he said. “It is an important point that stops the rot.
“We go into the next game in a different frame of mind. You do not want to be losing week after week, it drags every down around the entire club. It is nice to stop that run.”
But Clough was also left rueing yet another costly defensive error.
“To give a goal away again like we have done is absolutely staggering,” he added.
“All we have done the last two weeks is talk about the goals we have given away from individual errors.
“So therefore when you go on to the pitch as a player in that situation, you do not take any chances whatsoever. Why he took that chance I do not know.
“You can’t work on stuff like that, it is a player attitude thing. They have to take on what we are drilling into them every day, week after week - you do not make those mistakes.
“Without giving the goal away we might have gone and won 1-0.
“It was a much needed equaliser. Goals change games. It was even until they scored theirs and then they started bossing it and putting us under pressure.
“The second we got our equaliser we were looking like we were going to nick it, probably undeservedly, but we have lost four games undeservedly.”
The visitors had enjoyed the better of the limited first half chances with Jake Beesley twice going close in the opening 25 minutes.
Joel Coleman comfortably saved a long-range Stephen McLaughlin with chances at a premium.
Ryhs Oates was just unable to tap home a Jordan Bowery cross at the back post deep into stoppage time.
Max Taylor headed a corner over from just three yards out three minutes into the second half.
But Cashman fired Rochdale ahead after Matty Dunn took full advantage of a blunder by Kellan Gordon to pick him out.
Bowery curled wide before George Maris had a powerful shot blocked.
They got the response when sub Johnson slotted home from close range on 73 minutes from Ollie Clarke’s cutback.
Coleman made a great reaction save from Clarke on the stroke of full-time.