The Black Cats have recorded only one win on their own pitch since March, a run of 13 games in all competitions which has included defeats by Everton, Manchester United, Middlesbrough, Aston Villa and West Brom.
Chelsea, who have problems of their own, will try to extend that sequence of results at the Stadium of Light on Saturday and with the home fans becoming increasingly edgy, O'Neill has warned his players they will have to be brave.
The former Celtic manager told the Sunderland Echo: "It takes a strong player to play here for Sunderland at the Stadium of Light, I have often thought that.
"There are clubs up and down the country where it's tough playing at home. I managed a team up in Scotland for five years where you had to be a really decent player, with a strong mentality.
"I think it was the late Tommy Burns who said it was harder to play for Celtic than to play against them. I know exactly what he means.
"Here, it's demanding and you have to have plenty of courage and ability to play here. You have to have a good mentality and a bit of self-confidence.
"And then you need to go and win some football matches and put on a performance. That's very, very important."
O'Neill is also having to contend with injury problems which seem likely to rob him of the services of skipper Lee Cattermole with knee ligament damage for some time, while striker Steven Fletcher left the field at Norwich on Sunday with an ankle problem.
The Black Cats are yet to reveal the extent of the two injuries.