Dogged resistance earned Poyet's men a share of the spoils against the Premier League leaders at the Stadium of Light, although the likes of Jozy Altidore and Adam Johnson had late chances to win it for the hosts.
That left some fans wondering what might have been, although Poyet was more than satisfied with a point against a Chelsea team who remain unbeaten in all competitions this season.
He said: "I am realistic so I am pleased. To have the chance to get something against a team like Chelsea, first you need to defend - and do it properly.
"We did that. That's a minimum. We had chances at the end because there was space.
"You never know if it's fate or not but we need to be pleased with the performance. It was our best for a while."
The game's biggest incident came when Diego Costa was shown just a yellow card for an apparent elbow on Wes Brown, which came after the striker had seemingly kicked out at John O'Shea in the opening period.
Poyet refused to be drawn on the specifics of those incidents but did concede that Costa gives officials decisions to make.
He added: "He is always close to the limit. I think the decisions can go one way or the other.
"I haven't watched the video yet. They are 50-50s - one day they go for you and others they don't.
"If it was [Sunderland midfielder] Lee Cattermole, he would have got sent off for sure."
