O'Neill upset with "disappointing" Sunderland performance
Swans keeper Gerhard Tremmel had only one save of note to make from Sebastian Larsson's first-half free-kick, and although opposite number Simon Mignolet was little busier, Nathan Dyer passed up a glorious opportunity before Graham's big moment.
O'Neill said: "We played very disappointingly in the game. Coming on the back of a couple of great wins, I thought we were going into the game with plenty of confidence, and also with the weekend off, I thought we would be refreshed and really ready to go.
"But other than a spell just after half-time for a while, I thought Swansea, possibly without looking all that fantastically dangerous themselves, really dictated a lot of the game."