The Dutch were guilty of missing numerous chances on Saturday night as the match finished goalless after extra time in Salvador.
However, Van Persie and his teammates were able to win the resulting penalty shootout 4-3 to book their place in the semi-finals.
"Those misses could have been very costly, but our win is all that matters now," the striker is quoted as saying by Gulfnews.com.
"It's bizarre. We had too many chances. You have to stay strong and focused in such circumstances. We had to work hard to win this game."
The Netherlands return to action on Wednesday when they face Argentina for a place in the final.