McGowan's father James McGowan was last month found guilty in a Scottish court of the 1999 stabbing murder of his former brother-in-law.
McGowan says he and his brother Ryan, a Socceroos defender playing in China, have suffered fall-out from the conviction.
"We sort of pay the price, myself and my brother, a little bit in terms of the media and opposition fans and stuff like that," Dylan McGowan told reporters in Adelaide on Monday.
"I'm big enough to cop that on my shoulders and it's probably something that I shouldn't have to cop.
"But I will because that is the way of the world at the moment and people see fit that they want to discuss these sorts of things with you or shout out abuse at you."
James McGowan, 58, was convicted in the High Court of Edinburgh in mid-February of the 1999 murder of his former brother-in-law Owen Brannigan.
The court heard McGowan stabbed Brannigan 11 times in the neck and body and fled Scotland for Australia the next day. He was extradited in March last year.
James McGowan has been given an 18-year non-parole period for the murder.
"It has been a big year, especially off the field. It's difficult," Dylan McGowan said.
But the Reds centre-back, who spent four seasons from 2010 playing in Scotland, was reluctant to detail the spectator abuse.
"It's not something that I'm going to go on about," he said.
"It's football. I have copped plenty of abuse over my time - you should try playing in Scotland, it's a good laugh.
"But I don't want to give them any more fuel for the fire because there's enough there already that they like to have a pop at me for.
"The Adelaide fans have been fantastic for me and for that I will be forever grateful in this difficult time."
McGowan is set to exit Adelaide at the end of the A-League season but declined to expand on his expected move to an overseas club.
"I'm an Adelaide player for now... I will do anything to win football matches for this club so that won't change," he said.