Some thugs surrounded his car an hour after Saturday's defeat to Leicester, leaving wife Melissa and 14-month-old son deeply upset.
"There's a line people shouldn't cross and this is most definitely it, what happened on Saturday was horrendous," said Gregan.
"These people waited over an hour to abuse me and my family. I can handle any criticism, but when it's your family that are being sworn at it is out of order.
"My wife is due to give birth next weekend and I had my 14-month-old son with me.
"I don't want to complain about supporters, but picking on my wife and a little boy is beyond belief, it makes you wonder if it's all worth it," Gregan told the Yorkshire Evening Post.