Following a night that started with great expectation but ended in heavy disappointment, McLeish will need to rouse his men to greater levels of skill and passion in the Danish capital than they could manage in this uninspiring contest.
A goal from Todi Jonsson, the Faroese striker, after 50 minutes was the goal that broke Rangers’ hearts and left them with it all to do in the second leg in a fortnight’s time.
McLeish had called for his men to assert their grip on the match as early as possible and the opening minutes couldn’t have gone any better for Rangers.
It had taken Lovenkrands 14 minutes to open the scoring against Kilmarnock at the weekend; here he needed only half of that time to break the deadlock.
As was the case against Killie, it took a glaring error from the goalkeeper to hand the Light Blues the lead.
Mikel Arteta was chopped down wide on the left by Erik Mykland, but rose to swing in a tempting free kick that squirmed out of the grasp of Balazs Rabuczki in the visitors’ goal.
The ball sat up nicely for Lovenkrands lurking at the back post who made no mistake from around six yards.
It was an ideal start for Rangers and the home crowd sat back expectantly and waited for an onslaught that never materialised.
The Light Blues continued to dominate in terms of possession but struggled to find a way past a determined Copenhagen midfield and their well-organised back four.
The Rangers’ cause wasn’t helped by some eccentric officiating by Spanish referee Manuel Gonzales and his two officials who seemed determined to steal the limelight.
Twice the Danes were awarded corner kicks when it seemed no Rangers player had touched the ball and several home attacks were also cut short by some contentious decisions.
Arteta was seeing a lot of the ball in the midfield and sent in a vicious shot that spiralled narrowly past the post.
Mols then had a great chance to add to Rangers’ lead with a carbon copy move of the Light Blues’ second strike last weekend.
Arteta’s corner was headed on by Craig Moore where Mols struck the legs of the prone goalkeeper from all of three yards.
While content primarily to sit in and defend, the Danes were not shy in mounting lightning fast counter attacks, with Sibu Zuma and Thomas Roll Larsen linking up well.
Zuma in particular was looking lively up front and he jigged his way through several tackles after 33 minutes before firing in a dangerous shot that was well blocked by Stefan Klos.
The South African soon threatened again and this time only a desperate lunge from Zurab Khizanishvili halted his progress as the half fizzled to a close with Rangers unable to add to their slender lead.
Worse was to follow just five minutes after the re-start when Copenhagen netted the away goal that the Light Blues had dreaded.
A deflected shot fell kindly to Jonsson on the edge of the penalty box and his turn and sweet shot evaded the despairing dive of Klos.
That strike changed the whole complexion of the tie and, needing more goals, McLeish handed Nuno Capucho his competitive debut, withdrew Mo Ross and went with three at the back.
Capucho was followed onto the park 12 minutes later by Steven Thompson, with Ronald de Boer making way after a disappointing performance.
With the frustration audibly growing around the stadium, the Light Blues continued to press forward but with little reward.
They will need to play better in the second leg if they are to make it through.
RANGERS (4-3-3): 1 Klos; 21 Ross (Capucho 58), 3 Moore, 15 Khizanishvili, 18 Ball; 2 Ricksen, 6 Ferguson, 23 Arteta; 14 de Boer (Thompson 70), 10 Mols, 11 Lovenkrands
Subs not used: McGregor, Vanoli, Berg, Nerlinger, Malcolm
Booked: Ferguson (78)
FC COPENHAGEN (4-4-2): 16 Rabucki; 17 Tobiasen, 5 Albrechtsen, 4 Svensson, 3 Rooba; 25 Nooregaard, 7 Mykland, 8 Nielsen, 9 Roll Larsen; 12 Jonsson (Moller 32), 10 Zuma
Subs not used: Kihlstedt, Zivkovic, Bisgaard, Svard, Traore, Bech
Booked: Roll Larsen (28)
Man of the Match: Zurab Khizanishvili