Poyet's men were undone by a brilliant solo display from Eden Hazard, who scored twice and set one up, and he does not think they could have pushed Jose Mourinho's men any harder.
"Chelsea had to work very hard today to get the three points, we could not do more today," said Poyet.
"It was just little things like in the defending but you can't do that against teams like that."
Poyet admits he side could do nothing about Hazard, who produced one of the best performances he had seen as a manager.
"Eden Hazard was unplayable," said Poyet.
"I don't remember a player performing at this level against me, we tried everything, two men and double up, three on him and then tried another full-back.
"But he was great, the best I have seen this season."
Poyet insists Sunderland can take a lot of heart out of the performance, despite the result keeping the club bottom of the table.
"If we can play like we did today, and fight like today, we will still be in the Premier League for sure," he said.
"Today was an exceptional game of football.
"We are heading in the right direction but we have to confirm that with a win."