Keane joined Celtic on loan from Tottenham until the end of the season on transfer deadline day and O'Dea fears he could face similar problems if he is not careful.
"It's disappointing, but it's one of those things," said O'Dea, who is hoping to return from a hamstring injury in time for Saturday's SPL game at Aberdeen.
"It's part and parcel of living in Glasgow. I'll be a lot more careful in future or I just won't go out.
"I'm a professional footballer and some people like to pick fights with us. I don't usually go out that much anyway, so I'll just have to stay in more.
"Other players get targeted by people and that's what it's like. That's the problem when you only have two big clubs like Celtic and Rangers in one city."
O'Dea added in the Daily Mail: "It's not the first time it has happened and it won't be the last. Robbie has joined us now and he'll have to get used to it, too.
"Glasgow is a tough place to live and there are certain parts of the city you just don't go."