The win was secured by Titus Bramble's 27th-minute own goal, and although the Black Cats, who have now not won in eight games, rallied after a lacklustre first-half display, they rarely looked like snatching a point.
Bramble can count himself unfortunate - Robin van Persie's shot clipped full-back Phil Bardsley and looked to be flying wide until it hit his knee and nestled inside the far post.
O'Neill said with a smile: "I am as buoyant now as - I was nearly going to say as I have always been.
"What is it - the half-full or the half-empty glass? I'm even going to the three-quarters full.
"There's a real determination in the dressing room. The players are obviously disappointed, but they can take a lot from the second half.
"Yes, there is a determination about the players in there that we can do it."