The Whites needed to produce a better result than the Clarets to survive and the day eventually ended with the dream scenario of Leeds winning at Brentford and Burnley falling to defeat against the Magpies.
As part of an afternoon of continually checking events at Turf Moor, a Callum Wilson brace saw the Magpies to a 2-1 win against the Clarets as Leeds defeated the Bees by the same score through a Raphinha penalty and late Jack Harrison strike.
The two results meant Leeds survived their second season back in the Premier League with a three-point gap back to Burnley but Cooper admitted that his side had hoped for much more but that injuries and adversity had been no help.
Even on the final day, United were without six players at Brentford as Patrick Bamford missed out due to a positive Covid test, joining the injured Stuart Dallas, Adam Forshaw, Luke Ayling, Crysencio Summerville and suspended Dan James on the sidelines.
Cooper, though, says his men stuck together in tough times and issued a message both to United's supporters and also his family after a "stressful" period ultimately ended with Leeds staying up.
Speaking alongside Jack Harrison, Cooper was asked how it sounded that Leeds United would be playing Premier League football again next season, Cooper told LUTV: "It sounds unbelievable.
"I think we set out at the start of the season, we set out for a lot better than that.
"But after the adversity that we've had, the injuries we have had, it's been backs against the walls.
"That is a success in itself what we've managed to do today.
"I'm not one for celebrating stuff like that but, like I've said, the adversity and what we've been through as a group, we've stood together, we've never turned on each other once, we've had that belief in the squad and we needed that belief today going into the last minutes and this man pops up and what a finish."
Reflecting on where Sunday's events ranked in his moments over the years at Leeds as the Whites continually needed checks on events at Burnley, Cooper reasoned: "Me myself I took it upon myself.
"I knew what the other score was at half-time, obviously we were aware of the score and every ten minutes I was asking the boys on the bench what score is it, what score is it and it was just crazy.
"I think I need to apologise to my missus and my kids.
"Over the last six weeks, they've been walking on eggshells around me.
"It's been stressful, I'm not going to lie. It's been difficult times.
"But we come in every day, we work hard and if you do work hard and you keep knocking on the door then eventually things pay off and we're absolutely delighted to be playing Premier League football again and that's for the fans.
"They have stuck with us all season.
"The atmospheres they have generated is unbelievable and we don't deserve them at times.
"They've got us through again today so thank you very much and I hope they all get home safely and they can be proud of us today."