Spurs enjoyed 68% of possession against last season's champions and weighed in with 18 shots, six of which were on target, as well as winning 14 corners.
However, the Blues ended up surviving the Spurs onslaught and managed to convert their only two shots on target, both registered by Marcos Alonso, to leave the national stadium with all three points.
Pochettino told BBC Sport after the game: "I am disappointed because we deserved more but they were very clinical with two shots on target and two goals. We dominated and we were better but if you are not clinical, you can lose like today.
"We are one step ahead than last season. We were much better in every aspect of the game than Chelsea, they were just clinical. I am not frustrated or upset I am happy with the performance of the players. We are working hard, there are plenty of games to play."
When asked whether goalkeeper Hugo Lloris should have done better for the second Chelsea goal, Conte replied: "Sure, but that is football. It is about the team's performance. We were unlucky today, deserved more but we need to keep going."
The result means that Tottenham's 19-game home Premier League unbeaten run has come to an end, with Chelsea the first side to beat Spurs away from home since Southampton in May 2016.