The striker netted from close range 12 minutes after the break to claim just a second league victory of the season for Villa, while the Black Cats mustered only a single notable effort on target, and that six minutes from time.
O'Neill's men have now won just one of their last 17 league games but he is confident that a break will eventually come.
He told Sky Sports: "It was particularly difficult really. We threw everything at them today unable to break them down and unable to score a goal.
"We had so many balls in the area, you could hardly have counted all the chances, but you just need a break and I believe it will come.
"It's been a difficult time and we have got to see it through, but the players are capable of doing that."
When asked if he believes he has a few players who are not quite at their peak, the Northern Irishman replied: "I believe that's true. I think our creative players at this moment for one reason or another need a little bit of confidence. Things will turn and they will turn well for us.
"Overall the effort was fantastic and so was our captain Lee Cattermole."