Alex McLeish will be proud of the effort his team put in but the Gers boss will no doubt reflect tomorrow on the amount of chances his men passed up and wonder what might have been.
Peter Lovenkrands was Rangers’ busiest player but also the most culpable as he failed to find a way past United goalkeeper Tim Howard despite numerous attempts.
The return match at Old Trafford will give the Light Blues the chance to make amends but they will need to be sharper if they are to spring a shock on the English champions’ home turf.
The music and the atmosphere pre-match had signalled this was a European tie but there was more than a hint of the Light Blues’ recent league form in the manner that this match burst into life.
As was the case in the games against Celtic and Motherwell in the past fortnight, Rangers were allowed to enjoy almost exclusive possession of the ball without having the guile or creativity to pierce a cast-iron defence.
The home fans had read this script before – why play one pass if they could eke out five?
When they did get going, Rangers’ best moves came down the right flank, where Lovenkrands and Zurab Khizanishvili combined to good effect.
The Dane enticed John O’Shea into a reckless challenge after only 36 seconds – the Irishman was booked as a result – and went on to enjoy Rangers’ first decent chance of the opening period when he headed Michael Ball’s direct cross narrowly over the crossbar after 18 minutes.
By that time, however, United were already in front. With just five minutes on the clock, Craig Moore’s loose header was picked up by Phil Neville who swapped passes with Ruud van Nistelrooy before bursting into the box and sliding a low shot past Stefan Klos.
It was an early set-back for Rangers but to their credit they battled back and dominated the remainder of the half.
Lovenkrands’ made Howard work for the first time after only 24 minutes with a low drive before Paolo Vanoli screwed a shot wide from a matter of yards after another header from Lovenkrands had rebounded into his path.
Shota Arveladze, playing in a withdrawn role in the centre of the park, then launched a swerving shot narrowly over as Rangers pushed forward looking for an equaliser.
They were fortunate, however, not to fall two behind just before the interval when Ryan Giggs’ corner was nodded on by Mikael Silvestre only for Mikel Arteta to clear to safety off the goal line.
With United adapting a braver approach and venturing forward more often, the second half began with a flurry of chances for either side.
The English Champions were first to show and the hitherto subdued van Nistelrooy dragged a shot wide of goal before Roy Keane warmed the palms of Klos with a blistering drive.
Stung into action, Rangers then had three glorious chances to bring themselves level but couldn’t find a way past Howard.
From Arteta’s corner, Moore’s goalbound header was headed off the line by Phil Neville before only a last-gasp Rio Ferdinand tackle diverted Lovenkrands’ run on goal.
The Dane then headed straight into the goalkeepers’ arms from yet another Arteta corner as Rangers upped the ante.
McLeish took off the tiring Vanoli and his replacement Christian Nerlinger was soon in the action, breaking up a United corner and setting Arveladze free.
The Georgian made a lung-bursting run into the United half to feed Lovenkrands but the Dane shot tamely wide.
The last 15 minutes were nail-bitingly tense as Rangers threw everything forward in search of an equaliser, taking the risk of leaving gaps at the back.
With time ticking away, Lovenkrands missed another glorious chance when he dribbled his way into the box but dragged his shot agonisingly wide.
Like Rangers’ cause throughout the match, it was another case of so near yet so far.
They will have their chance for revenge at Old Trafford in a fortnight.
RANGERS (4-4-2): 1 Klos; 15 Khizanishvili (Ross 85), 25 Berg, 3 Moore, 18 Ball; 23 Arteta, 2 Ricksen, 16 Vanoli (Nerlinger 66), 26 Lovenkrands; 7 Arveladze, 10 Mols
Subs not used: McGregor, Hughes, Capucho, Ostenstad, Emerson
MANCHESTER UTD (4-4-2): 14 Howard; 2 G Neville, 5 Ferdinand, 27 Silvestre, 22 O’Shea; 3 P Neville (Butt 85), 18 Scholes, 16 Keane, 25 Fortune (Djemba Djemba 90); 11 Giggs, 10 van Nistelrooy
Subs not used: Carroll, Ronaldo, Fletcher, Forlan, Bellion
Booked: O’Shea (1), Scholes (72)
Man of the Match: Henning Berg