Manchester City’s Sterling, 24, was allegedly racially abused by a fan while playing at Chelsea in December.
The forward later said newspapers helped “fuel racism” by the way they portray young black footballers.
“Raheem was only saying what we all say in the dressing room,” said Rose, 28.
“It’s sad really but he’s 100% spot on with what he said,” Tottenham defender Rose told BBC Sport before England begin their Euro 2020 qualifying campaign against the Czech Republic on Friday and Montenegro on Monday.
“The stick he used to get from the media was bang out of order. When he put the [Instagram] post up about the media we were all over the moon with that because we all agree. Fair play to Raheem.”
Sterling’s much-publicised social media post pointed to headlines about team-mates Tosin Adarabioyo and Phil Foden buying houses.
The headline referring to Adarabioyo focused on how he spent £2.25m on a property “despite having never started a Premier League match”, while one on Foden said the midfielder had bought “a £2m home for his mum”, later adding he had “set up a future”.
Sterling has also drawn media scrutiny for a tattoo of a rifle on his leg, which he says refers to his late father, who was killed in Kingston, Jamaica.
“One of the few positive things about social media now is you have a voice and you can influence people,” Rose added.
“Now it’s not just boys in the dressing room talking about the media targeting Raheem, the general public have now seen it. We hope it changes but it doesn’t affect Raheem in any way, which we are all grateful for.”
Racial abuse ‘will not be solved overnight’
Chelsea winger Callum Hudson-Odoi is in Gareth Southgate’s England squad for the first time for the opening two Euro 2020 qualifiers. The 18-year-old faced alleged racist abuse while playing for Chelsea at Dynamo Kiev in the Europa League on Thursday.
Rose has previously said he had become “numb” to racial abuse and had “no faith” in football’s authorities to challenge it.
“I was only reading this morning about what Callum had gone through,” Rose added. “It will not be solved overnight.