The 25-year-old was on Tuesday replaced by French rookie Isack Hadjar as Max Verstappen's partner at Red Bull for 2026.
Having also been overlooked for a return to sister team Racing Bulls, Tsunoda will become a Red Bull test and reserve driver.
"I'm not finished yet," he wrote on social media.
"Finding out I won't have a race seat in 2026 was incredibly tough, but I'm determined to work harder than ever with Red Bull as test and reserve driver, and prove I deserve a place on the grid."
Tsunoda replaced New Zealand's Liam Lawson at Red Bull two races into this season, stepping up from Racing Bulls.
Since then, however, Tsunoda has scored 33 points in the world championship compared with Verstappen's 396.
The Japanese driver, who has been with the team since joining the junior programme in 2019, has competed in more than 100 grands prix and has yet to make a podium.
He currently sits one place and three points below Lawson in the standings.
"Life's full of setbacks, and this is mine," said Tsunoda, who made his F1 race debut in 2021.
"It's not going to deter me from being the best F1 driver I can be."
