Cooper returned from a recent knee issue for Wednesday night’s Premier League hosting of Chelsea who eased to a 3-0 victory which has kept Leeds in the drop zone with just two games left.
United were already 1-0 down when forward Dan James was shown a straight red card in the 24th-minute and the Wales international now joins Luke Ayling in being suspended for the remainder of the campaign.
Leeds also have Stuart Dallas, Adam Forshaw, Tyler Roberts and Crysencio Summerville out injured whilst Patrick Bamford is continuing his recovery from a foot problem.
The Whites were also dealt two more potential injury issues in Wednesday night’s defeat against the Blues as both Jack Harrison and Raphinha were taken off in the second half.
Cooper admits there is a strong sense of everything currently going against his Whites but United still have two games left in their bid to seal top-flight survival.
Sunday’s Elland Road showdown against Brighton comes next before the following Sunday’s last game of the season at Brentford and Cooper says there is only one way that United can react in their current plight.
The skipper has also issued a message of thanks to United's fans for their continued support during Wednesday night's reverse against Chelsea who condemned Jesse Marsch's side to a third-straight defeat.
“It’s tough, it’s tough to take,” admitted Cooper to LUTV.
“But you can either sit here and feel sorry for yourselves and do that or you can come out swinging and make a good ding-dong of it.
“We have to pick the lads up; we’ve got a massive game at home at the weekend.
“The fans again were unbelievable, honestly.
“We don’t deserve them at times so thank you very much, very much for that but we all need to pull together and make it a hell of an atmosphere at the weekend as they always do and we have got to go and produce on the pitch as well.
“It’s a massive game and let’s make a right good go of it.”
Cooper missed four months of the season between December and April owing to a hamstring injury but the captain returned in fine form, helping Leeds to a 1-1 draw at home to Southampton and then back-to-back clean sheets in a 3-0 win at Watford and a goalless draw at Crystal Palace.
A knee issue then kept the Scotland international out of both the home clash against Manchester City and the trip to Arsenal, both of which ended in defeat.
The Whites skipper came straight back into the side for Wednesday night’s contest against the Blues but Leeds fell behind after just four minutes when Mason Mount finished off a Chelsea break with a fine strike into the top-right corner from the edge of the box.
Cooper said: “It was a counter attack, and it’s a great finish, but it’s just difficult to take so early.
“I thought we started the game bright and, obviously, the goal changed it but we were still in the game.
“The red card changes it a lot; we have to obviously have a bit more of a negative approach to the game and sort of pick and choose when we go and try and nick something on the counter attack.
“It’s difficult against top quality opposition, it is, they kept the ball well.
“I thought we were resilient for long periods of the game but the quality of Chelsea came through.”
Cooper, though, now says Leeds must show qualities of their own via a determined fighting spirit in Sunday’s contest against Brighton.
Asked if it felt like everything that could go wrong was going wrong, Cooper declared: “It is. We are due a bit of luck, maybe a decision somewhere along the line and, hopefully, they cough up in the next couple of games.
“But from my point of view and my message to the lads is that we can’t sit and feel sorry for ourselves, we’re in a fight now and we know that.
“We’ve got to go and be positive and approach the game and get a result in any way possible.
“It doesn’t have to be pretty, it doesn’t have to be nice, we have to go and do it the Leeds way and, hopefully we can do that at the weekend and make a fist of it.”