The home side started with second choice holding midfielders Rafael van der Vaart and Nigel de Jong and it was the Swiss who had the best chance before the interval when unmarked Admir Mehmedi hit the side netting.
The Dutch improved after the break but had a Robin van Persie header denied by goalkeeper Diego Benaglio. The striker also missed the target after a fine defence splitting-pass from Wesley Sneijder.
The Netherlands face arch-rivals Germany on Tuesday in Hamburg, though without Van Persie who is being rested
Dutch coach Bert Van Marwijk defended his team after catcalls from the crowd during and after the match.
He told reporters: "This team has performed excellently for three and half years year and are widely admired for that. Today they had a bad day against a tough opponent and... they don't deserve such a reaction from our crowd.
"We are aware that we didn't play well, not dominant enough, though in the second half we had some good phases with good chances."
Tottenham star Van der Vaart had previously expressed his excitement at the prospect at returning to the home of former club Hamburg SV, but the midfielder suffered a slight hamstring injury and will now miss Tuesday's match.
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