Hiddink has now lost three of his four matches in charge of Oranje since taking the reins from Louis van Gaal over the summer.
However, the Manchester United striker refused to blame the change in coach for Sunday’s Euro 2016 qualifier defeat.
“That’s not fair to Guus Hiddink and his staff,” Van Persie told NOS.
“He’s a fantastic coach. We worked hard to get here in as good shape as possible. Iceland were looking for our mistakes.
“We made too many errors in possession and weren’t strong enough in duels.
“I still have hope. Nothing is decided yet, but there’s a lot of work to do. We’ll do anything. We don’t give up.”
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