Second half goals from Sebastian Larsson and James McClean ensured that The Black Cats made it through to the fourth round, where they will take on Middlesbrough in a North East derby.
O’Neill feels that the Stadium of Light fans will be delighted with the draw, and is eager to have a run in the cup to lift the supporters’ spirits.
“The last few supporters in the ground let out a big roar when the draw was made,” O’Neill told Sky Sports.
“It will be one that we look forward to. It’s a great tie for both sets of supporters and we are at home so we will see if we can make that count.
“The Cup is important to this club. We haven’t done well in it recently but I will try and put that right,” he commented.
The Northern Irish coach was also full of praise for goalscorer McClean, who he has been impressed with since taking over at the Wearside club.
“He has played three on the trot now and he’s been brilliant.
“In my first week here he played against Manchester United in a reserve game that I thought was going to be called off because of 70mph winds.
“The conditions were dreadful but he quickly came in to the game.
“He did brilliant on the night and he showed a real aptitude for it. We took a chance with him. He had a little bit of luck when he came on against Blackburn but he electrified the place and he has continued to do that,” he concluded.
By Gareth McKnight