Branislav Ivanovic and Pedro set the hosts on their way to a comfortable victory, and Allardyce admits that he cannot understand why his side started so slowly.
“I think we’ve gifted Chelsea the opportunity to be very good by our poor performance and they took full advantage of it,” he added.
“That’s what you expect with the squad of players they’ve got.
“We encouraged them so much that it was mind-boggling to me to see my players play with so much fear and so much worry about the opposition that they could hardly put one foot in front of the other.
“At least we got better when we changed the system, put the subs on, but by that time it was too late.
“Chelsea thoroughly deserved to win and, obviously, it’s a big result for them and a very poor result for us.”
Sunderland have had a worrying tendency to start slowly throughout the season, and they have been made to pay recently.
Watford and Chelsea have both raced into leads against the Black Cats, and overturning the deficit has proven too much for Allardyce’s side.
It means that they have been dragged back into trouble, with the Wearsiders now five points away from safety, after losing their last three outings.
Sunderland’s fixture list is doing them no favours either, as their next match comes against high-flying Manchester City on Boxing Day.