The former Liverpool goalkeeper was struck by a fan who ran onto the pitch seconds after Michael Tonge's equaliser for Leeds.
Kirkland was able to play on, but has insisted that more should be done to prevent similar incidents.
"I was gutted at conceding the goal and had my head down as I kicked the ball back down the field," said Kirkland.
"I was looking at the ground but when I looked up I caught a glimpse of someone running towards me. I thought he was going to give me some abuse but then he came at me with both hands. I was stunned.
"I felt the full force and I was shocked because you never know what could have been in his hands."
The FA have said that they will investigate the incident, and Kirkland has urged them to take action.
He continued: "I just want the authorities to look at what happened and take appropriate action, because sooner or later we could be talking about something more serious.
"It's not a nice feeling thinking my daughter saw me assaulted like that."
The incident overshadowed an entertaining game, which ended 1-1.