Charlton Athletic supporter Daniel Boylett, 36, of Eltham, was arrested after trouble broke out at the match on 23 September 2015.
He was found guilty at Croydon Crown Court of attempted damage for the attack on Kayla. He was also found guilty of violent disorder.
Boylett was released on bail to be sentenced on 28 April.
Crystal Palace, who are nicknamed The Eagles, adopted Kayla as a mascot in 2010.
Who is Kayla the Eagle?
The court heard handler Chris Belsey was walking around the Selhurst Park pitch with the bird on his forearm at the game.
Prosecutor Daniel Higgins said "three or four fans were shouting abuse" at the pair when one leaned over the barrier and "threw a punch".
He said Mr Belsey did not know if the punch had landed and Kayla "seemed unhurt", but "due to her delicate bone structure if she had been hit with force, her bones could easily break".
Four other men were on trial with Boylett over the trouble which marred the Capital One third-round tie.
Mr Higgins said there had been trouble "before, during and after" the game.
The first scuffles broke out as police escorted Charlton supporters to Selhurst Park.
One officer suffered a cut lip after being hit by what he thought was a bottle as rival fans tried to break the police cordon, the court heard.
At the end of the match, which Charlton lost 4-1, Donegan ran at police wielding a large yellow cone and had to be "subdued with a baton strike".
After his arrest, he told police he was "annoyed" as "we just got battered. I picked it up and let my anger out".
The jury were previously directed to acquit Cowcher, Boylett, Kitto and McConville on another count of violent disorder due to insufficient evidence.
A football fan has been found guilty of trying to punch Crystal Palace's bald eagle mascot during a cup game