The 36-year-old forward scored his 16th goal in World Cup finals against the Selecao in Belo Horizonte on Tuesday as his side thumped the tournament hosts 7-1.
Klose's strike moved him ahead of Ronaldo, who was in attendance, as the most prolific marksman in the competition's history, but the German was quick to remember the quality of the retired Real Madrid and Inter attacker.
"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."
The Lazio man conceded, however, that the Brazilian would have been disappointed to lose his record, particularly considering the pivotal match in which it occurred.
"Obviously it must be bitter for him that he was in the stadium when I overtook him in the match against Brazil," Klose added.
"Before he sent a message out 'Klose - welcome to the club of 15'. I can now send out this message: 'Miroslav Klose in the club of 16 and everyone's welcome to join'."
Germany now face Argentina in the World Cup final at the Maracana on Sunday.