Marcelo Bielsa's side surrendered a 1-0 first-leg advantage and lost 4-2 to Derby County on the night at Elland Road this evening.
The Leeds captain looked shaky throughout and was involved in a mix-up with goalkeeper Kiko Casilla on stroke of half time which led to Frank Lampard's side equalising on the night and reducing the aggregate deficit to 2-1.
Cooper also conceded the penalty which saw Derby move 3-1 ahead after 58 minutes, and former United boss Grayson believes that the 27-year-old defender, who's been brilliant for the most part this season, buckled under the expectation.
He told talkSPORT: "It's amazing what playoff situations can do to players. Liam Cooper has been outstanding all season and yet made a couple of errors. Leeds were on the back foot then."
It isn't the first time that Leeds have completely orchestrated their own downfall this season.
They had automatic promotion in their own hands with four Championship games left, but a disastrous Easter period saw Bielsa's side throw it away and consign themselves to the playoffs.
Derby will face Aston Villa in the final on May 27.
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