The 31-year-old announced his decision to quit Three Lions duty on Wednesday afternoon, bringing an end to a 13-year spell that saw him make a record 119 appearances for an outfield player.
There had been suggestions that Koeman persuaded Rooney to call it a day due to a potentially gruelling schedule for the Toffees, but the Dutchman claims that the surprise announcement was purely the player's doing.
"He's in really good fitness and it's always up to the player what is best to do," he told reporters. "I would have respected it if he had made a different decision. I think it is a good decision for him and a good decision for Everton.
"Wayne spoke to me about this. He had a talk with the national coach and he made his decision. He thinks it's the best for Everton. There's always the decision by the player and of course I respect that.
"I don't give him advice. I'm not the right person in his decision. Of course, if we reach the group stage of the Europa League and international duty - that's really a tough programme."
Everton face Hajduk Split in the second leg of their Europa League playoff tie this evening, protecting a 2-0 lead from last week.