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Two goals from Harry Kane and one each for Toby Alderweireld and Kyle Walker gave Spurs a 4-1 home win on Sunday.
"It is one of our best performances and results this season," said Pochettino.
West Ham boss Slaven Bilic apologised to Hammers fans for the defeat - only their second in 10 games.
"It hurts more because it was Tottenham," Bilic told the club's website. "I want to apologise to the fans because it's a special kind of game and tomorrow it's not going to be very good for our fans to go to work with the Spurs teasing them.
"The performance matches the result to be fair. They were better than us. They wanted it more than in a normal game, but we simply were not good enough to get anything, other than being defeated."
Bilic was without his "best player" Dimitri Payet, who has scored five goals and assisted three more this season but will be out for the next three months with an ankle injury.
"We knew we would miss Payet and we will be without him for a long time but we didn't lose 4-1 because he wasn't playing," added the Croat.
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Sunday showcased another high-pressing, energetic performance from Tottenham, who led 2-0 at the break thanks to Kane's neat close-range finish and Alderweireld's header from a corner.
Kane's second, soon after the break, essentially sealed the win before Walker added a well-taken fourth and Manuel Lanzini fired in a late consolation for the Hammers.
"I am very pleased with the performance and with the players. Congratulations to them," Pochettino told BBC Sport. "It was an amazing show and I feel very proud. We all feel very proud.
"The most important thing is that the players believe in the way we play and we share the same philosophy. Today was a big step forward because it was a very good example of how we want to play, and how we want to play in the future."
Mauricio Pochettino said he was proud of his Tottenham players after they produced an "amazing" display to beat West Ham and equal a club record of 12 Premier League matches without defeat.