Three Lions boss Roy Hodgson revealed after Tuesday's 1-0 win over Estonia that the 19-year-old told him he was "too tired" to start the game, and also questioned Liverpool's recovery measures.
But Johnson feels Sterling has been misrepresented in the aftermath, adding that "anyone with half a brain" would know the youngster would never turn down the chance to play for his country.
"I think club and country should support him," Johnson told reporters. "With Raheem, he is still growing and playing in the best league in the world every week. He is going to have a demand on his body.
"He wasn't tired as has been published. He was asked, 'How do you feel?' and he's said his thighs were tired. There's a difference between aching and actually saying: 'I'm tired and I can't play'. "
When asked if Sterling is suffering from burnout, Johnson continued: "That's the way it has been presented, but anyone with half a brain would know that's not the case. He'd play every week, if he could.
"You are never 100 per cent fit, certainly not when you are playing games every four days, you are going to play with knocks and pain and aches. And then your body gets used to it."
"He was asked a question and gave an honest answer, and got punished for it."
Johnson, though, does not blame Hodgson over the fall-out, which has involved Liverpool boss Brendan Rodgers and a number of other public figures, but questioned the need to publicise the matter.
"In hindsight you could probably handle most situations better," he added. "But I am sure they didn't mean to cause the reaction it caused. Unfortunately people jumped on and ran a few headlines."