Hiddink has tasted defeat in three of his four games since retaking the reins from Louis van Gaal, who moved to Manchester United after steering the Dutch to an unlikely third-placed finish at the FIFA World Cup.
The most recent loss came on Monday as Iceland eased to a comfortable 2-0 win in the Euro 2016 Group A qualifier thanks to Gylfi Sigurdsson's double.
Asked whether he is missing his club manager Van Gaal at international level, Van Persie responded: "Hiddink is a great manager so it's not fair to say that."
The Netherlands are third in their pool, six points adrift of table-toppers Iceland - although Van Persie has called for calm.
He added: "We must keep hope. Nothing has been decided yet. It's an honour for everyone here to play for Oranje. We won't give up."
Arjen Robben was less positive, admitting the Netherlands are "not very good" right now.
He admitted: "We have to start at zero again. We shouldn't pretend we're very good, because obviously we're not."
