Goals from Gabriel Jesus and Ilkay Gundogan put City 2-0 ahead after the 25-minute mark, before a second-half goal from Raheem Sterling cancelled out a reply from Christian Eriksen just before the break at Wembley.
"I am not going to complain about the penalty. I think that many things happen during a lot of games, sometimes it is for you and sometimes not," Pochettino told BBC Sport.
"In the end, if we analyse the game, they fully deserve the victory. We struggled to start in the game. When we conceded the penalty, we started to play.
"For sure they are going to win the PL but I'm disappointed because we didn't compete in the first 25 minutes. In football you always want to compete and win. We feel that we are close but it is not enough.
"Of course, when you are calm and relaxed, you think in the last few seasons we are improving. But we still need to improve to reach the last level which is the most difficult thing."
The defeat for Spurs sees them surrender a two-game home winning run against the Citizens.