The defeat leaves Holland six points off top spot in Group A and means they now face an uphill task of qualifying for Euro 2016 in France.
Both Van Persie and Blind played the full 90 minutes but were unable to help the Netherlands avoid a defeat which now means Guus Hiddink has an extremely difficult few months ahead of him.
Speaking after the game, Van Persie remained upbeat: “We must keep hope,” he said.
“Nothing has been decided yet. It’s an honour for everyone here to play for Oranje. We won’t give up.”
Van Persie also refused to undermine Hiddink when asked whether he missed having Louis van Gaal as his national manager: “Hiddink is great manager so it’s not fair to say that.”
Despite the poor performance, Dutch journalist Elko Born believes the issue was simply down to a lack of concentration on behalf of the players: “The Netherlands did not play well tonight,” he said.
“It wasn’t so much motivation or drive that was missing, it just seemed like the Dutch were not concentrating.
“They were constantly caught out by the Icelandic players, every move they made came one crucial second too late.”