The Whites played out a thrilling 2-2 draw with the Toffees in LS11 on Saturday afternoon as supporters returned at full capacity for the first time in 17 months.
Rafa Benitez's outfit opened the scoring in West Yorkshire on the half hour mark after a challenge from Leeds captain Cooper was overturned on review.
Referee Darren England initially turned away Dominic Calvert-Lewin's complaints as he tumbled to the floor in the box under pressure.
United, though, saw their skipper penalised after he was adjudged to have unfairly dragged the England striker to the floor by his shirt.
Marcelo Bielsa's men later levelled ahead of the half-time interval before the visitors went ahead once more in the second period through winger Demarai Gray.
Leeds then earned themselves a point with a little under 20 minutes to go in what was a frantic finish as Raphinha rifled a shot home emphatically to get the Whites off the mark in the top flight this term.
“Dom’s (Calvert-Lewin) initiated the contact, he’s got hold of my shirt and I’ve got a bit of him," Cooper said of the first half incident post-match.
"It’s one of those things. I was disappointed it was a penalty but I like to think these things even themselves out over the season. We can’t grumble about them, we move on to our next game now."
Asked about the result, he added: "If there’d been another five or 10 minutes we’d have won. We were in the ascendancy and I think we’ve had the chances. We’ll take a point, it’s a bit disappointing but obviously, if you can’t win, don’t get beat."