Rangers failed to take their chances as they slumped to a single-goal defeat to Maritimo in their Uefa Cup first leg.
Italian striker Gustavo Manduca pounced after Stefan Klos failed to hold a Leo Lima drive to put Maritimo ahead.
A Nacho Novo volley and a Dado Prso header struck the post either side of that first-half opener.
But Klos also had to produce a fine save to deny Leo Lima after the break, while Maritimo keeper Marcos Oliveira prevented Novo grabbing an equaliser.
Rangers had made one change from the side that drew with Hearts on Sunday, with Shota Arveladze replacing Paolo Vanoli for the trip to the sun-kissed island of Madeira.
Maritimo were protecting a proud record, having only lost one European tie on home soil - to Juventus - with Leeds United being among their victims.
But Rangers took the game to the Portuguese and Novo should have done better than to head wide after being found unmarked 12 yards from goal by a Chris Burke cross.
Former Motherwell defender Mitchell van der Gaag appeared to clip Novo inside the Maritimo box only for the referee to rule it was a dive.
The ball moved to the other end and Alan's low drive was well held by Stefan Klos.
A superb Fernando Ricksen cross found Novo 10 yards out, but the Spanish striker steered the ball off his chin and against the upright.
Luis Filipe rounded Craig Moore inside the Rangers box but sent the ball wide of the far post with only Klos to beat.
A Prso header flew just wide as the action moved from end to end.
Maritimo went ahead when Klos failed to hold Leo Lima's drive and Manduca followed up to drive the ball home from 15 yards.
Leo Lima almost made it two moments later with a curling drive that was tipped over the bar by Klos.
Novo was unlucky when he chested down a cross and stabbed the ball towards goal only for goalkeeper Marcos Oliveira to clear off his line with his foot.
Prso's header struck the post from the resulting corner.
A Leo Lima drive flew just wide of the Rangers far post before Novo broke clear only for his powerful shot to be blocked by the goalkeeper.
Klos had to produce a fine save to palm away an Alan drive as Rangers tired and Maritimo dominated in the latter stages.
Maritimo: Marcos Oliveira, Ferreira, Tonel, Van der Gaag, Briguel, Leo Lima (Zeca 84), Wenio, Luis Filipe, Manduca (Zumbi 73), Chainho, Alan.
Subs Not Used: Nelson, Bino, Souza, Fernando, Joel Santos.
Goals: Manduca 27.
Rangers: Klos, Ross, Moore, Boumsong, Vignal, Burke, Mladenovic, Ricksen, Arveladze, Prso, Novo (Lovenkrands 83).
Subs Not Used: Graeme Smith, Hughes, Thompson, Khizanishvili, Malcolm, Vanoli.
Ref: Johan Verbist (Belgium).