Rangers 1-3 Ajax
A harrowing first Champions League campaign in 12 years for Rangers came to a close with the ignominy of a new pointless record for the group phase.
Rangers needed an improbable five-goal swing to beat Ajax to third place and the Europa League. What they got was another painful reminder of the ruthless quality in this tournament.
Goals from Steven Berghuis, Mohammed Kudus and Francisco Conceicao made it six straight defeats for the Ibrox men, as a James Tavernier penalty left them with a goal difference of minus 20.
Rangers are the first Scottish team to go through the group phase without a point and become the 22nd side in the history of the competition to do so.
Dinamo Zagreb had previously held the unwanted worst record with a minus 19 goal difference from season 2011-12 - a tally matched by Viktoria Plzen this term but eclipsed by the Scottish Premiership side.
Injuries have hampered Rangers but the gulf between the Glasgow team and their Group A opponents has been stark.
The air was still thick with smoke from Ajax fans' pre-match pyrotechnics when the visitors struck. A slick move opened up the Rangers defence, with Kudus providing a neat lay-off for Berghuis to side-foot beyond Allan McGregor.
The home side responded in determined style, with former Ibrox favourite Calvin Bassey denying his old team-mate Fashion Sakala with a goal-line clearance.
However, further defensive frailties were exposed with Kudus given far too much time inside the penalty area and his shot going in via a big deflection off Leon King.
Now Ajax were brimming with confidence and it took a good diving save from McGregor to deny Steven Bergwijn before the same player drilled an angled shot narrowly wide.
That passage of play prompted loud boos from home fans fed up with a perceived lack of application from their side and there was another scare just before half-time as Kudus was close to turning in a mis-hit strike from Berghuis.
Supporters had to be content with cheering the odd hard tackle in a largely dreary second half as the hosts battled for a way back and Ajax dropped their tempo.
The impressive Kudus was denied a second goal after a VAR check for offside, while Scott Arfield's dipping volley had to be tipped over by Remko Pasveer.
Alfredo Morelos then somehow skewed his shot wide of an open goal before Rabbi Matondo was bundled over for a 87th-minute penalty, which Tavernier slotted down the middle for just Rangers' second goal in these six outings.
That looked like staving off the dreaded record until Conceicao was allowed to jink forward and drill in a third for Ajax.