The South American giants' World Cup campaign ended in deep disappointment, culminating in their earliest tournament exit since 1990.
"It is a great pain that we have not reached where we dreamed of together, you and us. Unfortunately, it didn't turn out how we imagined. It's part of the sport," Raphinha wrote on Instagram.
"The defeat won't always be what we want, but the pride of representing Brazil and of fighting to the end will never be erased. And for all our children who cry with us today, don't give up on your dreams.
"Perhaps you have watched this Cup imagining what it would be like to be there one day. Keep that dream in your heart.
"You are our next generation. Keep believing, training, persevering and loving football. It's dreams that Brazil has always lived, and it will be the dreams of you that will continue to write the history of our national team.
"I am honored to be Brazilian and to be part of this selection. Wearing this shirt and representing our country is a privilege that I will take with me forever. Regardless of the outcome, being part of this story is something I am extremely proud of."
Competing in Group C, the Selecao experienced a relatively sluggish start with a 1-1 draw against Morocco.
However, they quickly found their tactical rhythm to secure successive, convincing 3-0 victories over Haiti and Scotland, ultimately topping the group standings with seven points.
Moving into the expanded knockout rounds, Brazil edged past a resilient Japan side with a hard-fought 2-1 victory in the Round of 32. Unfortunately, their journey came to an abrupt and shocking halt in the Round of 16 against Norway.
Despite creating major chances, Brazil failed to capitalize, notably missing a first-half penalty through Bruno Guimaraes. Norwegian striker Erling Haaland ruthlessly punished their defensive lapses, scoring a clinical second-half brace to stun the South Americans.
A late penalty from Neymar deep in tenth-minute stoppage time proved a mere consolation, sealing a painful 2-1 defeat that left the global powerhouse eliminated far earlier than initially expected.
Neymar da Silva Santos Junior's international career ended with painful symmetry at MetLife Stadium, the same venue where an 18-year-old announced himself with a goal on his Brazil debut in 2010.
Norway have played down concerns over illness within their World Cup squad ahead of Saturday's quarter-final against England, with team doctor Ola Sand insisting every player is fit despite speculation of a sickness bug spreading through the camp.
England are monitoring the fitness of Reece James, Declan Rice and Marc Guehi ahead of Saturday's World Cup quarter-final against Norway after the trio missed team training on Wednesday.
Lionel Messi overcame the disappointment of an early missed penalty to inspire Argentina's remarkable 3-2 comeback victory over Egypt in their World Cup round-of-16 clash on Tuesday.
