The Dutch got their campaign off to a flying start on Friday as they hammered the defending champions in Salvador.
However, Van Persie is aware that the team still has plenty of work to do before they can be considered genuine contenders for the title.
"The tournament has barely started yet. We achieved an impressive result but we have a long way to go to win this tournament," the striker told FIFA.com.
"This is my fifth tournament and I know how these things work: the euphoria vanishes just as quickly as it appears. So we have to make sure that we hold on to it – not only for the people and fans, but also for ourselves."
The Netherlands are back in action on Wednesday when they play Australia.