The Bayern CEO said his side "showed too little passion" as the Spanish giants marched into the Champions League final with a 5-0 aggregate win.
Title holder Bayern came into the Champions League semifinal second leg attempting to erase a 1-0 deficit but was ruthlessly caught out at the other end as two Sergio Ramos headers and a double from Cristiano Ronaldo saw Madrid ease to victory.
The nature of the loss will again raise questions about Guardiola’s philosophy and Rummenigge said some of Bayern's weaknesses were highlighted by Carlo Ancelotti's approach.
He told Sky: “We showed too little passion to cause problems for the opponent. We were unlucky to concede from two set pieces. After that it was clear that Real would probably go to the final.
“You have to state it clearly: Real Madrid is a great team at the moment. And they have shown us some of our limitations today. Real Madrid has limited our offense. And they have regularly caused trouble for our defense with their quick players. This was one of those matches. We must keep our nerve."