Leeds said it will ban Cawley for life from the team's Elland Road ground once the banning order expires, but felt the sentence was too lenient.
"While we are pleased to see justice brought so quickly, our one disappointment is that we feel the sentence could, and should, have been considerably longer," Leeds said in a statement.
Kirkland, who plays for Wednesday and won his one cap for England in 2006, needed medical treatment after being knocked to the ground by Cawley amid violent scenes at Hillsborough, which was all broadcast live on British television. Kirkland told police it was like he had been "hit by a ton of bricks."
