Grayson, who used to manage the Seasiders, saw his new side triumph due to Tom Clarke's late header, before a pitch invasion from home fans at the full-time whistle led to a steward being trampled on by a police horse.
"You don't want people to be running on the pitch and I would have preferred them to stay behind as the football club might get in trouble over what's happened, but hopefully there's not been too many people seriously injured," Grayson said.
"Hopefully it was only supporters being boisterous and there was nothing too intense or damage done to anybody as you see how much it meant to everybody at the football club.
"The result shows everybody what it means to the football club. I thought it was a cracking cup tie with a great atmosphere with some good football and good defending.
"I thought we played some good football, with great shape and organisation and worked hard, passing the ball when we could in what was a tight game."