The 23-year-old was booed by a section of his own fans when he came off the substitutes’ bench during the 3-1 victory at Fulham on Sunday.
"James will deal with it. It's to do with the issue of last week [not wearing a poppy]. It's a free choice here in this world," O'Neill told reporters.
"James has lived with a lot of things, he's getting death threats now."
Sunderland claimed a much-needed victory against the Cottagers, with the hosts reduced to 10 men in the first half following Brede Hangeland dismissal for a challenge on Lee Cattermole.
Steven Fletcher, Carlos Cuellar and Stephane Sessegnon all found the back of the net for the away side to give the scoreline a convincing look, but O'Neill admitted that the sending off played a major part in his team's victory.
He added: "The sending off of course changes the dynamic of matches. You saw it yesterday with Tottenham and you have to try and take advantage of that and I thought we were able to do that in the second half yet we were never able to put Fulham away.
"We've been given the directives. I didn't know how many times we need to be told about it. We've been guilty ourselves with Cattermole getting sent off but sometimes I don't understand players now.
"There is a better chance of winning a football match with all your players."