The manager of the football club is said to have told his bosses that he was "angry and disgusted" at the footage.
The clip shows a McCoist-like figure tumbling from the top of the club's Ibrox stadium, smashing the club crest on the way.
It was broadcast just before live TV coverage of Rangers' League Cup tie win over Motherwell on Wednesday.
BBC Scotland said the sequence was a creative reworking of the opening scene of hit US drama Mad Men.
However fans on Twitter condemned the images and the club said it had been inundated with complaints.
One fan wrote: "I was absolutely stunned. It's absolutely disgusting and totally unjustified.
"There's nothing remotely funny about dep-icting the manager jumping from a window."
A club website statement said: "The Light Blues have been inundated with e-mails and phone calls from supporters who are, rightly, furious with the way the programme began."
It said the montage depicted a Rangers official, "clearly manager Ally McCoist", falling from a window and added: "While the manger is known for his good sense of humour, he is angry and disgusted by the BBC's treatment of him personally and of the club."
BBC Scotland said: "The creative animation, however well intentioned, may not have appealed to everyone. There was no intention to cause offence."