With only five games left and a harder run-in than Chelsea it still looks a tall order this season for Spurs, who face north London rivals Arsenal at White Hart Lane on Sunday.
Yet the way they persevered against an obdurate Palace side to grind out three crucial points it was hard to disagree with the Argentine manager, who has turned Tottenham's young side into one consistently challenging near the top.
"The team are now showing we are ready," Pochettino, whose side buckled at the death last year after chasing Leicester City hard, told reporters. "We are ready this season to fight and, next season, we'll be even better.
"We are showing that we learned a lot from last season as a team. That is so important because last season was a big challenge. To improve on that season, that was difficult.
"Last season, the team were fantastic, playing well, and it was a massive challenge to improve again."
Christian Eriksen's 78th-minute winner - an unstoppable dipping low shot - earned Spurs a victory and silenced the doubters who suspected Saturday's FA Cup semi-final defeat by Chelsea would stop them in their tracks.
They were not at their best but have now won eight successive Premier League matches and have 74 points -- a club record in the Premier League and will go into Sunday's derby with Arsenal still believing they can catch Chelsea.
At the very least Champions League qualification looks nailed on, as does finishing above Arsenal for the first time in 22 years, although Pochettino said that would not be uppermost in their mind in Sunday's north London derby.
"We are not thinking about being above Arsenal," he said. "Our challenge now is to try and reduce the gap to Chelsea again and think about bigger things than only to be above Arsenal.
"Now we have reduced the gap again to four points, but every victory is not to send a message to Chelsea. After every victory, the most important thing for us is you build your confidence, trust and belief.
"To win big trophies and achieve big things, your mentality must be bigger. You must think about bigger dreams. Big dreams. It's important to have them."
Meanwhile, Crystal Palace manager Sam Allardyce fears on-loan defender Mamadou Sakho could miss the rest of the season after he was carried off on a stretcher.
Sakho, on loan from Liverpool, injured his right knee while stretching to make a tackle on Harry Kane. The 27-year-old immediately signalled that he was in trouble and was carried off after treatment.
With fellow central defender James Tomkins having sustained a serious injury during the 2-1 victory at Liverpool on Sunday it is a further blow to Palace who are not yet safe from the drop despite six wins from their last nine games.
Palace matched title-chasing Tottenham before the break but faded in the second half.
