"We could have lost it in the first 15 minutes, " Netherlands coach Bert van Marwijk said.
Van Marwijk had arrived at his prognosis after speaking to Van Persie on the phone.
Van Marwijk claimed this week the 26-year-old Dutch striker could be fit for Arsenal by "the beginning of April".
"It's a little bit strange to stand here now, we haven't quite overcome the disappointment yet, " said coach Bert van Marwijk.
Kristjan Orn Sigurdsson pulled a goal back for Iceland with two minutes remaining, but Bert van Marwijk's team comfortably secured the victory.
Despite the Dutch being in a commanding position in qualification Group Nine, Hutton reckons the pressure is all on Bert van Marwijk's Oranje.
Just three lasted more than 12 months: Louis Van Gaal at Bayern Munich, Reynald Denoueix at Real Sociedad and Bert Van Marwijk at Borussia Dortmund.
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Dutch Coach Bert Van Marwijk has enjoyed great success by starting with a defensive midfield partnership of Mark van Bommel and Nigel de Jong.
"Things went wrong now and again but we took the initiative and when we scored to make it 2-1 we had confidence and you saw how well we could play, " added Van Marwijk.
Head coach Bert van Marwijk has infused the Dutch team with many of the virtues traditionally associated with Germany, where he coached Borussia Dortmund from 2004 to 2006: Today's Netherlands team is well-drilled, disciplined and, above all, hard-working.
Van Persie is not the only player carrying an injury to be included in Van Marwijk's squad, with Liverpool's Dirk Kuyt, Mark van Bommel, Khalid Boulahrouz, Wout Brama, Eljero Elia, Theo Janssen and Ruud van Nistelrooy also called up.
Dutch coach Bert van Marwijk -- who lost out on the chance to have become the first coach since 1970 to have led a side through World Cup qualifying and the finals unbeaten -- conceded Spain had deserved to win.
Van Marwijk's side showed signs of life when Van Persie latched on to a long ball over the top and played in substitute Rafael van der Vaart, who saw his low shot pushed away before Robben fired the rebound over.
The Arsenal forward, who has played just three times for the Gunners this season, made a successful return and played for his country at the World Cup in South Africa last summer as Bert van Marwijk's side reached the final.
"I think Spain are playing the best football overall but Germany are perhaps the best team at this championship, " continued Van Marwijk, who took over as Netherlands coach in 2008 and has now led the side on a 14-match winning streak.
However, goals from Sneijder - allowed to stand despite Robin van Persie appearing to be in an offside position - and Robben restored the Netherlands' lead going into the final 15 minutes and Van Marwijk's men held on, despite Maxi Pereira's stoppage-time curler.
It gave Netherlands coach Bert van Marwijk and his side a deserved victory, but one they rarely had to be at their best to secure against opponents that worked hard but lacked the composure to capitalise on the few chances that fell their way.
Uruguay coach Oscar Tabarez's team had time to launch a few balls into the Dutch box but van Marwijk's side survived and it is they who will go forward hoping it will be third-time lucky for them in a final following their defeats in 1974 and 1978.
Cheered on by an army of Oranje fans, Dutch coach Bert van Marwijk saw his side struggle to find their feet in the early stages, with their only sight of goal being wasted when Dirk Kuyt fired wastefully over after keeper Fernando Muslera had punched Sneijder's cross straight at him.
Van Marwijk's men have a 100% record in South Africa - matching their impressive achievement in winning all their qualification games for the tournament - and have now gone a Dutch record 23 games unbeaten, but there remains discontent amongst the Oranje Army, who feel their side are not winning with sufficient style.
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