While host Chris Rock was making his opening monologue Sunday night, Eaton tweeted why "does it always have to be about black and white? (hash)American".
Rock's comments referred to the lack of black nominees at the Oscars, and Eaton said his intention was to discuss equality. Some Twitter followers -- Eaton has nearly 35,000 -- took offense to a statement they felt was vague.
"I feel terrible," Eaton said. "I mean no harm and I apologize. I should not have even gone into that realm.
"In my baseball world, we have equality. Everybody in this room I respect and love, and everybody has an opportunity."
Eaton said he is re-evaluating his dealings with social media.
"I want to have a connection with people and I may step back for a little bit," he said.