The Black Cats were put to the sword at Stamford Bridge, after they made a very slow start in the contest.
Chelsea raced into a 2-0 lead within 13 minutes at the weekend, and Allardyce was very frustrated with his side’s performance in the first half of the match.
"I have to be honest, I saw so many poor performances in the first half that I could have changed almost all the outfield players," he said.
“I haven’t got that luxury.
“I have said to the players that they have to take more responsibility for their own performance and be more consistent.”
Sunderland were also guilty of starting slowly against Watford in their most recent home fixture, and it has become a worrying trait of the squad.
If Allardyce’s side are to get out of trouble, they will need to make sure that they start putting in 90 minute performances, as they are in dire need of victories.
Sunderland are already five points away from safety, and they are in danger of being cut adrift with Aston Villa unless they start picking up wins soon.
Unfortunately for the Black Cats, their next fixture comes against Manchester City at the Etihad Stadium on Boxing Day, and they cannot afford to start slowly in that match if they are to cause an upset.