The Black Cats get their cup campaign underway against League Two side Morecambe on Tuesday in the second round of the League Cup, and O'Neill is eager to get off to a good start.
The former Aston Villa manager cited last season's FA Cup quarter-final replay against Everton as a memorable occasion and, although they lost that match, the atmosphere whet his appetite for a repeat.
"The cup tie is very important for us. We had a taste for the cup last year and the atmosphere that night against Everton in the replay was extraordinary. It showed just what it means to the people here. We would love to do well," said O'Neill.
"We have a home tie and really want to make the most of it. We just want to give it a real go and show people what we want to do. I have not had the chance to see Morecambe myself, but we have reports and we will look at video coverage of them.
"We want to do really well in the cup competitions."
Morecambe progressed to the second round by beating Championship side Blackpool 2-1 earlier this month.