The former Germany international watched the game alongside the Blancos supremo, who had nothing but praise for the performance of the Bavarians' No.1
The Bavarians went into the game in the Spanish capital leading 2-1 up after last week's first leg at the Allianz Arena but they were left reeling after conceding two goals to Cristiano Ronaldo inside the opening 15 minutes.
However, Arjen Robben levelled the tie on aggregate from the spot at the tail end of the first half and Neuer then played a key role in Bayern's progression to next month's final in Munich by saving two penalties during the visitors' 3-1 shoot-out triumph.
"Real president Florentino Perez was sitting next to me and said, 'Manuel Neuer is the best keeper of the world'," Rummenigge told reporters after the game.
"We had a very bad start to the game. But it was the most emotional game of my career - and my career has been going for 40 years now.
"We are very proud and happy to be in the final. This is fantastic!"
Bayern president Uli Hoeness was also full of praise for Neuer's contribution but revealed that the shoot-out had almost been too much for him, admitting that he thought Jupp Heynckes' men had blown it when Philipp Lahm missed from the spot to allow Madrid right back into it.
"Manuel Neuer was great," he enthused. "I thought I would die after Lahm missed the second penalty! It was hard because we had been two goals ahead.
"Today it was the game of all games: Bayern Munich against Real Madrid. Something like this is only every few years. The favorites, Barcelona, are also out so we´re probably slight favourites for the final [against Chelsea].
"The greatest experience you can have in football is to play in a World Cup final or the final of the Champions League. And it´s great to play the final in your own stadium."
Bayern Munich are bidding for the fifth European Cup success, two years after being beaten by Inter in the 2010 final.