The Black Cats were completely outplayed by the Reds at Anfield and O'Neill suggests the result comes down to the fact he has a very small playing roster which has felt the effects of a hectic festive schedule.
"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."
Raheem Sterling opened the scoring in the 19th minute before Luis Suarez netted either side of half-time to condemn Sunderland to 14th position on the Premier League table, just four points above the relegation zone.