David Moyes was left to salute a breathtaking injury-time save from Thiebaut Courtois as Sunderland came close to ending Chelsea's winning run.
The Sunderland boss thought Patrick van Aanholt's strike from the edge of the box was destined for the keeper's top corner until the Belgian flew to his right to give the leaders a 1-0 win.
"I thought it was in and I expected the ref would have blown for time after it," said Moyes.
"It would have been ideal, they wouldn't have had any time after that.
"It was a really good save."
Courtois had also denied the Black Cats at the start of the second half when Jermain Defoe set up Adnan Januzaj with the keep saving superbly to his left.
"Their goalkeeper made two great saves, the second one obviously got all the plaudits because of the type it was," said Moyes.
"We got better as the match wore on and we finished the game quite strong, but we didn't have enough to get something out of the game."
It was Chelsea's 10th victory on the trot, Cesc Fabregas's expertly-finished 40th-minute goal taking Antonio Conte's impressive side six points clear at the top of the table.
And while the result kept the Black Cats bottom of the Premier League, the fact they were inches away from taking a point will have given great encouragement to Moyes.
Other results went Sunderland's way with Hull City and Swansea conceding three goals at Spurs and West Brom.
"The players gave everything, they did the best they could," added Moyes. "I just thought maybe we were going to get one."
Conte was thrilled to see his side achieve the perfect 10, admitting it was down to Courtois, while also praising Fabregas who came in for a rare appearance in the starting XI.
"Sunderland had a chance at the end, but Thibaut made a great save," said the Italian. "I'm very happy for Cesc, it was only the third game he's started."