Sneijder claimed on Tuesday he wanted to talk with the Arsenal striker about the set-piece taken, and missed, by Van Persie in Holland's quarter-final defeat to Russia.
Van Persie told AD Sportwereld: "When you want to invite an international colleague, you do that by phone and then you can speak.
"If Wesley had called me he would have been welcome. We could have had a fine talk. But I am amazed about the way Wesley handled it now.
"What is the use of such a talk if before it you tell the media and the audience what your problem is?
"I had expected more class and personality from him. Real personalities don't need a magazine or newspaper to make their point clear."
The Arsenal striker claimed Sneijder should have brought the matter up sooner, adding: "We could have talked about it in the hotel, after the match, if needed also during breakfast."