Rogers opened the scoring in England's 2-1 UEFA Nations League victory over Croatia on Wednesday, with Harry Kane also finding the net.
Palmer was left out of Thomas Tuchel's squad after the England manager raised concerns about his limited opportunities to impress.
The 24-year-old, who also missed out on World Cup selection, withdrew from September's international camp through injury.
However, Rogers was quick to defend his childhood friend, firmly rejecting claims that Palmer lacks commitment to the national team.
"He wants to be here,” Rogers told BBC Radio 5 Live.
"He wanted to get called up and he wanted to come and represent his country as he always has done.
"It has nothing to do with England or not wanting to play with England. It's a nonsense really that people are questioning someone that wants to play for England. It's a lie.
"You see the joy and smile on his face, how much he loves the game, so I honestly don't get it and he doesn't get it."
