The 23-year-old came in for criticism after opting not to sport a Remembrance Day poppy on his shirt during the Black Cats' 2-1 defeat at Everton last weekend.
McClean was introduced by O'Neill as a second-half substitute in Sunday's 3-1 win at Fulham and received a mixed response from the travelling Sunderland supporters.
Following the victory O'Neill backed McClean to cope with a few jeers and revealed the Republic of Ireland international has also received death threats.
"James will deal with it (the booing). I think it is to do with the issue last week, it's a free choice in this world," he said.
"James has lived with a lot of things - he's getting death threats too now so that doesn't help."
It is understood that police are investigating the threats which were directed towards McClean on Twitter, although the player no longer uses the social networking site.