Tottenham booked their place in the last 16 of the competition with a memorable 3-1 victory over Madrid in Group H at Wembley on Wednesday.
Dele Alli, suspended for the first three pool matches, scored a brace, while Christian Eriksen was also on target as Spurs condemned Zinedine Zidane's Madrid to their heaviest Champions League group-stage defeat since November 2008.
The surprise win against the Spanish and European champions follows Tottenham's impressive 1-1 draw in last month's reverse fixture, and Spurs boss Pochettino lauded his players after the final whistle.
"I'm very proud of my players and I congratulate them. I'm so pleased for Dele and our fans," Pochettino told BT Sport.
"The victory is so important for us and the players. It's a win over Real so it's great for the club and fans.
"There's a long way to go until the end of the season. What's important is trying to achieve our challenge and target.
"Of course, this win gives us great belief for everyone and confidence. We are now in the next stage of the Champions League. But now it's so important to compete against Crystal Palace [next weekend]. As a manager you can't stop thinking."
Pochettino was delighted with Alli's impact, but was left to rue an apparent hamstring injury for Toby Alderweireld.
"I told you yesterday [Tuesday] that Dele was coming. It's important for him - his debut in the Champions League this season. It's important he felt good," he added.
"I feel a little bad for Toby Alderweireld we have to assess it [his injury]."