Ben Gladwin and Michael Smith both grabbed doubles and substitute Jonathan Obika netted what turned out to be the crucial goal as they advanced 7-6 on aggregate having won 2-1 at Bramall Lane on Thursday.
But that only tells the half of the story with United having reduced the deficit to just one goal on three separate occasions with two goals coming in the final minutes in a thrilling conclusion.
And Cooper was lost for breath after the final whistle as his side moved a step closer to ending their 15-year absence from the second tier.
"I really cannot put into words what I have just seen," he said
"It was a freak, I'm sure it will be talked about for decades.
"It was like two heavyweight boxers trying to knock each other out
We kept scoring, they kept scoring
If we kept playing it could have been 10-10.
"It was the most ridiculous game of football you'll ever see
Brilliant goals and rubbish defending.
"I must give credit to Nigel Clough and his players, it was an unbelievable game of football."
Preston now await in the Wembley final later this month after they cruised past Chesterfield in the other semi-final and Cooper admits the likes of Jermaine Beckford, Joe Garner and Paul Gallagher will be relishing the chance to tackle the Robins.
"I'm sure Simon Grayson was rubbing his hands together watching it and with the firepower at their disposal I'm sure they'll fancy their chances," Cooper added
"But on the Wembley surface we'll fancy ours.
"The players have a couple of days off and then we'll be back at work
We have just got to enjoy the night and the feeling of getting to Wembley
I'm pleased and delighted we are there but the work starts now
"I'm very proud of them and proud because at the start of the season we were written off as relegation fodder
Even to get to Wembley is a magnificent achievement for us.
"We know we have our faults and we play a certain way and at times we have to concede and we know that
But we are not bad going forward, we can score goals and entertain."
For Clough it was play-off heartache once again but the former Derby boss was heartened with the way his side kept going before eventually just falling short.
"In the first 15 minutes it could have been 3-3, but they put their chances away and we didn't," he explained
"The fact we were still going in the 97th and 98th minutes was encouraging.
"You cannot describe how disappointed we are."
Source : PA