Ighalo made history when he scored the only goal of the game to secure the win for the Hornets, but the Black Cats were made to rue missed opportunities late in the game as Jermain Defoe and Duncan Watmore came close to an equaliser but failed to find the net.
Allardyce believes that his side struggled in the early stages of the contest, and has admitted that he was wrong to claim that he could see enough goals in the team to keep his side in the division.
He told reporters: “We are all extremely disappointed today. We could have made the gap so much smaller, instead it has grown.
“We had to change the system after 20 minutes or so because it wasn’t working, because players weren’t playing to their best.
“When I opened my big mouth a couple of weeks ago and said I had enough goals, I think I should have kept it shut.”
The Black Cats remain in 19th place in the table following their defeat.