Emmanuel Adebayor and Roberto Soldado scored either side of the break before former Spurs midfielder Kevin-Prince Boateng pulled a goal back for the Bundesliga club.
Pochettino handed Eric Dier his debut and the 20-year-old impressed in central defence alongside Younes Kaboul.
"It was a tough game, Schalke are a very good team and we can only say congratulations to the players," said Pochettino. "We had some good periods in the game. We played well.
"The team is showing a lot of energy. This is our style, our philosophy and now we have a week to go until the start of the season.
"Eric is still young but he has a lot of potential. He did well, we're very pleased and now we recover, one day's rest and we then train hard all week to prepare for West Ham."
Pochettino was introduced to the home fans before kick-off with new signings Dier, Ben Davies and Michel Vorm.
"It was our first time in front of our fans at White Hart Lane and it was fantastic. I say thank-you to all of them."