Leon Bailey's brace consigned Bayern to a 2-1 home defeat on Saturday and brought an end to Flick's perfect start as interim boss.
The champions are now three points adrift of RB Leipzig as their Bundesliga title defence continues to splutter almost a month on from Niko Kovac's dismissal.
Concern over the widening gap and the sudden availability of Mauricio Pochettino led to the suggestion that Bayern could hasten their search for a new head coach.
But Rummenigge insisted the latest setback would not alter the club's opinion of Flick and hinted the caretaker coach could yet remain in charge for the rest of the season.
"The most important thing in football is the quality of play, the game plan and we have that with Hansi Flick," Rummenigge told reporters.
"For me, nothing has changed after last night's game. We're very satisfied with him. We've agreed that we will continue until winter.
"After the last game we will sit down and discuss it and possibly continue beyond that."
Bayern have four Bundesliga fixtures and a Champions League game against Tottenham to negotiate before the mid-season break.
The loss to Leverkusen was their first since the 5-1 failure at Eintracht Frankfurt that spelled the end for Kovac.
Rummenigge said of Saturday's match: "It was the best Bundesliga game of the season but unfortunately ended with the wrong result for us.
"We have to forget the defeat and carry on with the same quality of play."
Flick's side head to high-flying Borussia Monchengladbach next Saturday.