Piastri finished second behind Verstappen in the season-ending Abu Dhabi Grand Prix, but third in the overall standings, while third on the night secured Norris his first title by two points.
"He is a future world champion. Both of our guys won seven races, drove brilliantly, supported each other," Brown told Sky Sports television.
"It's a cruel sport, things sometimes go your way, sometimes don't. I'm excited to go racing with these two drivers next year."
McLaren let their drivers race on equal terms and, despite talk of 'team orders' possibly coming into play, did not have to ask the Australian to move aside for Norris to deny Verstappen the championship.
"We let them race until the end. Most people thought that would be impossible to pull off. It's a dream racing with these two guys," said Brown.
At the chequered flag, Brown spoke to the disappointed driver over the team radio as he was being consoled by his race engineer.
"What a season, what a season. You're a star. Seven wins. We love you. We'll do it again next year. Thank you Oscar for everything you've done. What a year," he said.
"Oscar, very proud of you. Awesome. What a team player. We go again next year. See you on the podium."
Nico Rosberg, the 2016 champion who won his title on a tense night in Abu Dhabi after a battle with Mercedes teammate Lewis Hamilton, suggested in his role of Sky television pundit that the American could have toned down his message.
"Maybe Zak could have had a little more empathy there, rather than celebrating," said the German.
"He could have said 'next year will be your year', but it's difficult for Zak because he's so ecstatic at the same time."