The Benfica midfielder is joining Bayern this summer after extensive talks with United.
Rummenigge told WAZ: "I like the structured fee, because it is really good shopping. This is the market. If you want to have a man with world-class potential, then you must go into the water. And much earlier than has previously been the case.
"Otherwise these players are gone. And there is now a nation with almost infinite money in the market, which raises prices. The boy also had an offer from Manchester United, and if the transfer had not taken place so quickly, he would have ended up in England."
Rummenigge also says they fought off United last year in their battle to keep Thomas Muller.
"We had an insane offer last year from Manchester United, but not for a second was it an issue. We could have made the biggest transfer in the world's history."