After opening their Euro 2016 qualifying campaign with a defeat to Czech Republic, Netherlands came from behind to beat Kazakhstan before losing 2-0 in Iceland.
The results leave them third in Group A, six points off second, but Van Persie revealed he had engaged in a productive conversation with Hiddink, who took over from Louis van Gaal following this year's World Cup.
"It was a good, frank and honest conversation," he is quoted as saying by Algemeen Dagblad. "It was a critical talk, but it had to be. I understood that Hiddink will talk with other guys too.
"Everyone [from the national squad] is convinced it has to be different and better.
"The coach showed me what he wanted to see different and better. He showed a huge drive. He was sharp, hard sometimes, also to me. But it should be like that.
"I have a good feeling about the conversation. Although it was very serious, I felt a lot of trust."
"Klaas and I spoke extensively about it," he added. "We're both winners and have a lot of respect for each other as football players.
"I do understand that a moment like that drives the whole discussion. It is showed widely to the audience and people have an opinion about it.
"Maybe we had to deal with something like that a bit smarter. But it happened in the heat of the moment."
