Piastri missed out on a podium due to an untimely safety car from his point of view but he did secure his best-ever F1 finish of fourth, while Norris held off Lewis Hamilton for second.
Piastri also vaulted up the drivers' standings with 12 points added to his tally but Brown had high praise for his team principal Andrea Stella after the race.
Lando Norris claimed his first Silverstone podium thanks to a stellar defensive drive in the closing laps
Brown: Stella is awesome
“This guy is awesome," Brown said of Stella to Sky Sports.
"The way he inherited what we had at the start of the year, recognized the challenges that we had, put in a technical restructure, promoted people from within, because you know while we’ve made some bigger hires that are joining, they haven’t joined yet.
"So, this is still the work of all the men and women under Andrea’s leadership, and they put their head down."