Rangers went from the joy of scoring first to the despair of falling 3-1 behind and then to the frustration of being unable to find just one strike in 37 minutes to qualify for the last eight on the away goals.
Of course it just had to be Pierre van Hooijdonk who orchestrated the defeat with two stunning freekicks and a cute cross for Feyenoord’s third goal, scored by Bonaventure Kalou.
However, some of Rangers problems were self-inflicted and that will hurt McLeish as much as anything else, the prime example being when Neil McCann was sent off for mouthing off to the referee when Rangers were playing 10 men in De Kuip, which translates as The Tub.
The inclusion of McCann was certainly a clever one as the Scotland winger fired Rangers into the lead after 25 minutes but he blotted his copybook when he needlessly attracted a red card 18 minutes from time for dissent.
It had started pretty well for the Ibrox men. Although the Dutch side came at them, with Amoruso marshalling the back line Rangers looked solid.
In saying that Shinji Ono – Feyenoord’s scorer at Ibrox in the first leg – should have given them the lead after four minutes when dangerous winger van Persie picked him out with a cross from the left but the Japanese star headed over the bar.
Of equal importance to Rangers was McCann’s crucial challenge on Brett Emerton in nine minutes after the Austrlian threatened to burst into the box on the right side.
Rangers should have had a penalty a minute later when Lovenkrands was clearly bundled to the ground by Patrick Paauwe after a great burst into the box from the left but German referee Herbert Fandel was derelict of his duty when he failed to award it.
The Ibrox men then sufffered another nervy moment when van Persie and Ono combined again in 13 minutes but Amoruso managed to make a vital block to divert the ball away for a corner.
Rangers had weathered the early Feyenoord storm and began to impose their own game. And when they won a freekick in 25 minutes they got the breakthrough they craved thanks to the quick-thinking of Barry Ferguson and the ability of McCann.
Feyenoord were disorganised after Paul Bosvelt brought down de Boer and Ferguson speedily clipped the freekick into the box where McCann took it brilliantly on the volley to fire Rangers in front.
The lead lasted for 10 minutes, however, when van Hooijdonk struck with deadly precision and, horrifyingly for the bench, he repeated the feat a minute before half-time.
It was Wilson’s needless challenge on van Hooijdonk in 36 minutes which allowed Feyenoord back into the game and changed the course of events.
Van Hooijdonk punished Wilson and Rangers in the worst way possible, curling a trademark freekick over the wall and into the bottom left corner of Stefan Klos’s net.
Just before half-time the former Celtic star did it again after Vidmar was judged to have pulled him down and Rangers cursed their luck.
Amoruso tried to help out by running back towards the goal-line as van Hooijdonk took aim but he only seemed to confuse the issue and the ball sailed into the bottom left corner for the second time.
By this time Ronald de Boer’s involvement in the match was over. He had been relatively ineffectual and the gamble to play him clearly did not pay off.
Incredibly, Rangers went 3-1 down barely a minute into the second half and the European adventure looked dead and buried.
Rangers simply failed to deal with Bonaventure Kalou as he burst in from the left and cracked a low shot which cannoned off the right hand post. Van Hooijdonk collected the loose ball and whipped over a cross which Kalou headed into the net.
Remarkably, Rangers were given a lifeline when Patrick Pauuwe hauled down Mols in the box in what was a last-man challenge to concede a penalty and suffer an automatic red card.
Ferguson, just as he did in first leg, showed marvelllous compsure as he slotted the ball into the left corner with consumate ease and celebrated in front of the delirious Rangers fans.
It was game on now as Rangers had 37 minutes to try to conjure up and equaliser against 10 men to win the tie on away goals.
It looked as though Lovenkrands would provide it when he was presented with a glorious opportunity by Claudio Caniggia in 63 minutes after the Argentinian brilliantly got away from Emerton to cut the ball back.
However, the young Dane pulled his left foot shot wide of the target from only 14 yards out and the Feyenoord fans heaved a sigh of relief.
Rangers still had time, but McCann’s crazy display of petulance in 72 minutes must have sickened McLeish as it took away the numerical advantage.
McCann did look to have been fouled by Brett Emerton and was justifiably annoyed but it still does not excuse his behaviour, having been booked in the first half.
McLeish then threw on Tore Andre Flo as he fought to get the goal they needed to take them through to the last eight, but it was Mols who had the best chance.
He was released clean through on Edwin Zootebier on the right side of the box in 81 minutes and beat the keeper but his shot flew into the right side netting.
Rangers battled valiantly to find the goal they wanted by Feyenoord managed to stand firm.
In the end it was a rotten night in Rotterdam as the European campaign was ended and McLeish suffered his first defeat as Rangers manager, but it was an incredible match.
The Rangers boss now needs his players to dig deep and maintain their focus on the domestic front.
FEYENOORD: Zoetebier; Emerton, Loovens (Sprockel 86), Paauwe, Rzasa; Kalou (Smolarek 78), Bosvelt, van Wonderen, van Persie (Elmander 90); Ono, van Hooijdonk. Subs not used – Timmer, Aros, Leanardo, Smolarek, Korneev.
Sent off: Pauuwe (53)
Bookings: Emerton (78)
RANGERS: Klos; Vidmar (Flo 74), Wilson, Amoruso, Numan; Konterman, de Boer (Mols 38), Ferguson, McCann; Caniggia, Lovenkrands. Subs not used – McGregor, Dodds, Kanchelskis, Ross, Hughes.
Sent off: McCann (72)
Bookings: Vidmar (29)
Ref: Herbert Fandel (Germany)
Man of the match: Barry Ferguson
Moment of the match: The skipper’s ball forward for McCann’s goal.