Victor Wanyama, signed from Southampton in June, headed home in the 83rd minute at White Hart Lane to give Spurs a 1-0 victory and their first three points of the campaign.
Pochettino's men had drawn three and lost two of their previous five league matches, after ending last term on a sour note and handing the title to Leicester - and second place to arch rivals Arsenal.
"I think it's very important to recover this feeling because the end of last season was hard, tough," the Argentinian said
"Today was good to forget last season and to look forward
This is a different season
I'm very happy now with the performance of all the squad, all the players."
Tottenham looked to be heading for another frustrating afternoon after both Harry Kane and Vincent Janssen, deployed together for the first time, missed chances to break the deadlock.
Wanyama, however, making his home debut, was in the right place at the right time, nodding home from close range after Kane had met Erik Lamela's corner.
"I'm very happy with Victor because I was a player and it's very important to score in your first home game and feel the love from your supporters," Pochettino said.
Hugo Lloris' hamstring injury meant Kane was handed the captain's armband and he was also given a strike partner, with new signing Janssen taking the place of Dele Alli.
Pochettino said Alli had been ill and missed training on Tuesday and Wednesday.
Janssen was tidy in his link-up play and industrious off the ball, but the Dutchman's best chance ended in disappointment, after he skewed a finish when put through one on one.
"It was the same last season with Harry," Pochettino said
"I'm worried when it's impossible for them to have chances to score.
"When, like today, Vincent had lots of chances, it's about luck or being a bit more clinical
He showed very good energy, he played well, I'm very happy with his performance."
Pochettino relied heavily on Kane last term but also lacked the option of playing two strikers together, particularly at home and against opposition intent to sit deep.
"I remember when I arrived here, I wanted him Harry to play with another striker," Pochettino said.
"You could see Harry was more free
He had a lot of chances to score, to shoot - a lot, a lot - more than at Everton (last weekend's 1-1 draw)
I think it was a very good combination."
For Palace, this is a second consecutive 1-0 defeat and, just as against West Brom last weekend, Alan Pardew's side lacked a focal point up front.
Christian Benteke's move to Selhurst Park - for an initial £27million, plus add-ons - was announced just a few hours before kick-off, but came too late for the Belgian to be involved.
Pardew believes his new signing can make the difference.
"We had a great spell after half-time but, when you come to Tottenham, you have to score in that spell
That's the issue, and the signing of Christian is to address that," Pardew said.
"One thing that's always impressed me about him is he gets the goals you'd expect, but every now and then he gets a rabbit out of a hat as well.
"That's what you need on days like today
One moment would have changed the whole course of the game and, in that 20-minute spell, he could have done something for us."
Source : PA
Source: PA