The former Manchester United star is under pressure after Sunderland’s third successive loss at home.
“I ask myself every single day if I am the right man for Sunderland,” he said.
“I asked myself this morning and I said that I was. Tomorrow morning if the answer’s no we will have to look at it.
“I have to be honest in my assessment. It’s not about what’s best for Roy Keane. It’s Sunderland football club.
“I might wake up on Monday morning and think I’m the right man. On Tuesday it might be different.
“I’m the manager of this football club and ultimately I’m responsible and I’ve never shied away from that.
“That’s part of being a manager and that’s why I take full responsibility for today and the run we’re on and everything else.”