Giovanni van Bronckhorst's men finished bottom of Group A as their miserable campaign was rounded off with a 3-1 defeat at home to Ajax.
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Ajax went 2-0 up at thanks to goals from Steven Berghuis and Mohammed Kudus, the half-time whistle sparking a chorus of boos among the Rangers fans at Ibrox.
James Tavernier halved the deficit with an 87th-minute penalty but Francisco Conceicao restored the Dutch outfit's two-goal lead.
Rangers lost all six group matches, scoring just twice and conceding 22 in the process.
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And this sees them reach an unwanted feat of being the worst side to ever compete in the Champions League.
talkSPORT's Jason Cundy began his famous 'Has Anyone Seen?' opener on The Sports Bar by going through the Rangers squad as well as calling out famous fans including Ally McCoist and Gordon Ramsay.
After calming down, Cundy said: "What's going on in Scotland? What's happening up there?! Someone tell me.
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Jamie O'Hara responded: "Well they're out of their depth, aren't they? They're out of their depth.
"But you can't go down as the worst team in Champions League history, that's not acceptable. The players they've got, the size of the football club that they are, that's not good enough."
The result will raise questions about Van Bronckhorst's future at Ibrox but the Dutchman appeared to suggest the fixture scheduling contributed to his side's defeat.
When asked about his side's lack of intensity, Van Bronckhorst told BT Sport: "Their [Ajax's] league is thinking about their players. They played their last game last week on Wednesday and they come here really fresh.
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"Of course we played a game, we have some injuries. It was tough today but we tried and these are teams who are competing for several years at this level and this is our first time in 12 years."
But when asked if he feels the Scottish Premiership needs to do more regarding their fixture scheduling among Champions League matches, Van Bronckhorst appeared to backtrack.
He added: "You asked me the difference today, they haven't had a game at the weekend, that's the difference. I don't say we need help, I just say that they had a free weekend.
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