Tom Clarke nodded his first North End goal since his summer arrival in the 87th minute to send Simon Grayson's side through to round two at the expense of his old club.
But at the final whistle, hundreds of home fans swamped the pitch, prompting police horses to enter the fray and disperse the unsavoury end to the Lancashire derby.
A steward appeared to be trampled by a police horse following the invasion of the Deepdale pitch as he helped to clear it of fans.
The steward, wearing a hi-vis jacket, looked to have been struck by the horse as it cantered across the pitch, while another horse - also helping with crowd dispersal - seemed to clip him as he lay on the ground.
Lancashire Police confirmed they were looking into the incident.
Ince said the issue requires drastic attention.
"It's an absolute joke and I wondered if we have enough stewards," he said.
"You see enough situations where fans run on a pitch and I can understand fans' excitement, but there have been enough frightening things that have happened to players that we need to stamp down on it.
"There were three or four hundred Preston fans, so who knows what could have happened? Has it got to take something else to happen before we listen? That's not just Preston but it's the whole football community in general. We need to knuckle down on this.
Source: PA
Source: PA