Kirkland appeared to be punched by a Leeds fan who entered the field in the wake of Michael Tonge's 77th-minute equaliser, while unsavoury chanting also marred the night.
A large number of the Leeds fans housed in the Leppings Lane End sang about the child abuse charged which were dropped against Owls manager Dave Jones in, while former broadcaster Sir Jimmy Savile, now the subject of a similar police investigation, seemed to be heralded in song.
The Wednesday fans also stoked things up with songs about the two Leeds fans killed in Turkey in April 2000, with the Leeds supporters responding by throwing bottles onto the field and clashing with police.
"They are vile animals," Jones said. "You talk about racism, the chanting, that's a form of racism. And then (for the Leeds players) to go and wave at them... not in my book. You don't wave at them after that.
"I thought it had gone out of our game. The authorities have to look at it and sort it. I'm talking about an incident when we should be talking about the football. We're talking about vile animals. That's what they are. We talk about racism, but that, we need to sort that."
Leeds issued a statement after the game pledging to hunt down the man involved in the Kirkland incident.
Refusing to accept just one Leeds fan had been in the wrong, regarding the chants which rang out midway through the first half, Jones said: "It wasn't just one chanting. That was from their area too. I've had it for 12 years. It's just upsetting that they're allowed to do it. They should be banned from every away ground."
Neil Warnock called for Kirkland's assailant to be given a prison sentence as he described the events at Hillsborough as "an absolute disgrace".
The former Sheffield United boss told Sky Sports 1: "I felt embarrassed to be a manager when I saw that.
"I thought it was an absolute disgrace.
"I think they should get the guy and prosecute him and put him in prison.
"He (Kirkland) went down like a ton of bricks but that doesn't make a difference. Nobody should be on the pitch doing that.
"I hope we can make an absolute issue of it.
"He spoiled everything for everyone. I've not enjoyed that when I see a moron like that.
"I am not proud of being Leeds manager when I see that. I don't mind the rivalry between us - there was a great atmosphere.
"To see things like that on the field of play there is no place for it - I am absolutely embarrassed."