Cattermole was sent off for the fifth time in a Sunderland shirt in the midweek Capital One Cup tie against MK Dons.
O'Neill is disappointed that he must do without Cattermole for the next three Premier League matches, including the derby clash with Newcastle United.
The Mackems boss told reporters: "He is obviously very, very sorry, but 'sorry' doesn't help us now, not only over that particular game itself, which we could have lost, but the games coming up now.
"He does so many good things for us, both as a player and as a captain as well, but you can't be that rash.
"I always think you can learn if you really want to. I have always felt Lee, even though we have had a joke in here about it before, is capable of learning."
Cattermole begins his suspension this weekend as Sunderland go in search of their first league win of the season against Wigan Athletic.