The Knicks captain and 2026 NBA Finals Most Valuable Player spoke Monday at the team media day before training camp began.
"Not being satisfied is the biggest takeaway moving forward," Brunson said. "We just have to find a way to turn the page and move on."
It won't be easy after an off-season celebration like no other for a franchise that struggled for so long before returning to the top.
"Honoured and grateful for all the opportunities that have come about. It was the longest shortest summer ever but it was well worth it," said Brunson, who hosted Saturday Night Live's season opener last weekend.
"It's cool to feel the energy and it makes you want it even more."
Brunson, however, stressed that after ending the long Knicks title drought, this season will be a different quest.
"Last year we took everything one day at a time," he said. "We know what it takes, going through the same mindset for this journey.
"It's a new journey. It's a different journey. The approach has to be the same if not better."
Brunson averaged 28.4 points, 6.1 assists, 3.2 rebounds and 1.2 steals a game in the Knicks playoff run, capped by a 4-1 series victory over San Antonio in the finals.
He expects fans will see early on if the Knicks still have what it takes to capture the crown.
"The first couple weeks of the season are going to show us who we are and where we are," Brunson said. "No matter what we're doing, playing great or playing bad, how are we going to be able to learn.
"We'll find a way. We'll hold each other accountable. We'll learn and we'll be better."
Knicks big man Karl-Anthony Towns has goals as the 2026-27 campaign begins next month.
"Just get back to the drawing board, start at 0-0, be hungry, be willing to do whatever it takes again and to win it again," Towns said.
"To repeat, it's going to take an even greater sense of discipline and execution. We're going to have to be even better than what we showed in the playoffs.
"All of us are aware of that. We're going to have to bring a whole 'nother level to the table if we expect to have a chance to repeat."