Van Marwijk's highly-fancied side created 28 opportunities, hitting the post through Arjen Robben and having two penalty appeals turned down, but Michael Krohn-Dehli scored the only goal of the game at the Metalist Stadium on Saturday evening.
Van Persie was preferred to Klaas-Jan Huntelaar in the starting line-up and, despite his failure to make the most of the numerous chances that came his way, van Marwijk insisted the blame for Holland's lack of goals should be shared around.
Speaking at his post-match press conference, the Oranje coach said: "It was not only Robin van Persie. There were maybe four, five, six players who had a lot of chances. And the referee had also a chance to give us a penalty.
"I'm not looking for excuses. I'm just trying to give answers to the questions."
The result threw Group B - dubbed the 'Group of Death' - wide open, with Germany and Portugal both also vying to advance to the quarter-finals.
The Dutch next face Joachim Low's Germany on Wednesday, and van Marwijk recognised the added importance of that game given Saturday night's result.
He continued: "The players really wanted to do something with all the chances but the ball just didn't want to go in. We put the substitutes on [Huntelaar and Rafael van der Vaart with 20 minutes left] and were even more attacking - we had even more chance after that - but this is the game.
"We were really determined, but you have to score that goal, of course. When there's a penalty that doesn't go in your favour, that's unfortunate but that's part of the game.
"We just have to beat Germany. That's not going to be easy but that's the goal now and everyone knows that."
Denmark coach Morten Olsen claimed his team were the better side and deserved their win.
"We said it before the game - if we have to beat one of these teams, we have to reach a high level to get good individual form and a good team performance - and that happened," he said.
"Of course, the Dutch team had some chances but I thought we also had chances. We had good positional play and trusted our own way of playing football.
"That was especially important against a Dutch team who like to dominate. It was important to show how and why we qualified for this tournament.
"You saw a Danish team who overall were the better team and also over the last 10 minutes were better physically than the Dutch team - that was very important."
Asked if he was worried after Holland made a particularly bright start to the contest, he replied: "Sure, but football is not only 20 minutes. Its 90 minutes and more."
The Danes next face Portugal in Lviv on Wednesday.
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