Raheem Sterling's opening goal for the Reds followed by a brace from Luis Suarez was more than enough to consign the Black Cats to defeat.
And O'Neill had no complaints as he saw his team fade during their fourth game in 12 days after tough encounters against Manchester City and Tottenham in the past week.
"They were too strong for us today, they deserved to win the game," O'Neill told Sky Sports.
"And we just ran out of steam. We've probably got the smallest squad in the Premier League. I think it was just one game too far for us tonight.
"We started out very brightly indeed and put them on the back foot.
"Once they got the first goal, of course, it opens channels up for them and they exploited those."