The incident occurred after Thornton drove to the basket midway through the third quarter, falling to the floor and almost sliding into the advertising sign.
As the American guard looked up hoping for a foul call, the offender poured beer in Thornton's hair.
"That has to be dealt with," Cotter said.
"I'd be really ashamed if my club did that.
"This is 2015, not 1974. That's all I should say about it. But that's dropkick behaviour. I mean, really, how unsophisticated and how much of a drongo do you want to be? It shouldn't happen in the first place."
Beveridge said many players don't mind some verbal interaction with fans.
But the former Perth Wildcats coach was disappointed that line was crossed on Wednesday night.
"There's nothing wrong with a bit of banter and hometown sledging of the opposition, but what happened tonight was just plain stupid and disrespectful, and fans have to remember what is and what isn't acceptable behaviour," Beveridge said.
"I fully endorse the decision to eject the bloke. That's the only option available when something like that happens and escorting him out for everyone to see sends a clear reminder to all fans.
"The good thing is that the overwhelming majority of basketball fans understand and accept those boundaries and were lucky that those kinds of things very rarely occur. I'm confident it was a one-off situation that won't happen again."
Illawarra's win boosted their record to 5-6 ahead of Saturday night's second leg of their round eight double - a home game against Townsville.
Beveridge will still be without regulars Tyson Demos, Cody Ellis and Rhys Martin and hopes to have the injured trio back for next week's round nine meeting with competition leaders Melbourne.
The Kings remain last on the ladder with three wins from 12 games.
-AAP
