Marcos Alonso's brace ensured the three points for Antonio Conte's side, as well as the bragging rights in the London Derby, despite only having two shots on target.
Pochettino believes it was the host's profligacy in front of goal which cost them the three points, with 18 shots in total and six on target.
"The difference was they were clinical in front of goal, two shots on target, two goals," said Pochettino after the game.
"I am happy with the performance, we played really well and deserved more. It is difficult to accept today, but they were more clinical and I think we played well.
"I am not frustrated, I am disappointed. The objective was to win the game, which was impossible, but playing the way we did, we will win a lot of games.
"We dominated the game and created the better chances and sometimes we were a little bit unlucky today.
"This is only the beginning of the season and we need to work hard to improve and in that way, we can win a lot of games."
Chelsea's winner came after Hugo Lloris failed to keep out Marcos Alonso at his near post but Pochettino refused to blame his goalkeeper for the defeat.
"Football is about play, feel free, sometime success, sometimes not success, that is football and I am happy with the performance of everyone," he said.