Cawley, 21, from Cheltenham, appeared at Sheffield Magistrates' Court and pleaded guilty to assault and invading the pitch during a highly-charged game at Hillsborough which ended 1-1.
The court heard he had been the subject of two football banning orders in the past, which he had breached four times. In addition to his prison sentence he received a five-year banning order.
Cawley told police he had drunk several cans of Stella Artois and three-quarters of a litre of vodka before even travelling to Sheffield for the match, and a further seven to 10 pints of cider after arriving in the city.
Prosecutor Paul Macaulay told Sheffield Magistrates Court that the man was so drunk he only realised what he had done when he later saw himself on TV.
Leeds have banned the unemployed labourer for life and publicly criticised the leniency of the sentence.
"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 on their website.
Leeds also issued a statement apologising for the attack on Kirkland immediately after the match and the Football Association and South Yorkshire Police launched their own investigations.
An FA spokesman said: "We commenced our own investigation straight after the game and have spoken to both clubs in order to ascertain what exactly happened on Friday night.
"There will also be the referee's report to help us with this. There is no place in the game for this type of behaviour. We feel whoever is found guilty should be dealt with severely by the courts and handed a lifetime ban."
During the match, Leeds supporters are also believed to have sung tasteless chants about Jimmy Savile as well as targeting Wednesday boss Dave Jones with some disgraceful songs.
Jones, who described Leeds fans as "vile animals" after the 1-1 draw, qualified his statement on Monday, saying: “I apologise for tarring Leeds fans with the same brush, but look at it from my point of view: that one person ran on and attacked Chris Kirkland.
“But it wasn’t just about one person: after he’d done it, he was being slapped on the back as if he was a hero. I didn’t hear any of the other Leeds fans booing him. Who bought him his ticket, when he was a banned fan? Who hid him? Who sat next to him?
“It wasn’t just one or 40 or 400 Leeds fans chanting like they did. It was thousands. And when people say to me it’s just football banter, that doesn’t wash. Nobody should be subjected to vile abuse, and fans shouldn’t chant vile things at each other.
“I was angry with the whole situation."
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