The Bavarians blew a 1-0 lead in the closing stages of the match, before missing a penalty in extra time, and eventually losing in a penalty shoot-out.
"When I wake up, my first thoughts are always about the defeat against Chelsea," Rummenigge stated to Welt am Sonntag.
"The pain within our club is so strong, stronger than it was after we lost to Manchester United in the final in 1999.
"I feel that the defeat is going to haunt us for a long time to come. I lost two World Cup finals - 1982 and 1986 - and from my experience, I know that time heals wounds."
Bayern finished the 2011-12 campaign without a trophy as Borussia Dortmund pipped them to both the Bundesliga title and the DFB-Pokal.