Klose's strike in Germany's 7-1 semi-final triumph over Brazil was his 16th across four tournaments.
It moved him ahead of Ronaldo, who was in attendance, as the most prolific marksman in football's biggest tournament.
"He was an outstanding player," Klose told reporters at Germany's training base.
"I play in Italy and everyone I've ever talked to there said that Ronaldo was the best player that ever played in Italy. For me he was the most complete player ever."
Klose concedes his contemporary may have been disappointed to see his record fail first-hand.
"Obviously it must be bitter for him that he was in the stadium when I overtook him in the match against Brazil," added Klose.
"Before he sent a message out 'Klose - welcome in the club of 15'. I can now send out this message: 'Miroslav Klose in the club of 16 and everyone's welcome to join'."