Cattermole, 23, has a reputation for being hot-headed when on the football field, having been sent off six times in his professional career so far.
The latest of those red cards came last weekend in the Tyne-Wear derby after referee Mike Dean handed the midfielder his marching orders following a verbal exchange post the final whistle.
The incident, which has resulted in a four-match ban, has led to fresh conjecture over whether Cattermole should be Sunderland's skipper. But, when asked about whether he has considered relieving Cattermole of his duties, O'Neill said: "No, absolutely not, no.
"I was asked a few weeks ago if I thought I had cured Lee and I'm afraid I stared into the abyss on that one. But on a serious note he has been absolutely fantastic, really terrific, whenever he has played for us.
"I am told he has taken on the role of the captaincy and does a lot of things here that I wasn't aware of, really good things around the football club like getting players to particular functions.
"But the sending-off is very disappointing. Lee will have to try to learn from that because they are major games he is missing at a very, very important stage of the season. There's no getting away from that."