Rangers missed out on a place in the group stage for the first time after they were held to a 2-2 draw by Benfica.
The tie went into extra time after a close-range finish from Emma.
A solo goal from Canada's Cloe Lacasse was the only goal of the game.
The hosts could not deny the defender's sending off.
The Portuguese champions reached the group stage for a second successive season after Victoria Esson's own goal denied them a more convincing victory.
Despite making sweeping changes to their weekend line-ups, both sides returned to familiar lines.
It looked like a move of attacking intent by the host head coach.
In the first half, there was no need for defensive cover as Benfica dominated.
It signaled a wave of attacks that had the visitors pinned back in their own half after Ana Vitoria forced a near post save on Esson.
Esson was twice at full stretch to deny Andreia Faria from long range and then saved bravely to keep the game alive.
Lacasse had a chance to score in front of an open goal, but he missed.
The one-way traffic continued after the break, but Benfica's efforts on goal became less accurate as the game went on.
It took Malky Thomson's side until the 76th-minute to threaten and, when they did, substitute Watson fired straight at goalkeeper Rute Costa, while fellow bicyle failed to hit the target.
The aggregate score was level when Costa failed to hold a corner.
The full-back was shown a clean pair of heels three minutes into extra time as Lacasse strode into the penalty box and fired past the exposed Esson.
The game was in the balance until the second yellow card of Alves gave Rangers the advantage.
Formation 3-4- 3.
13Sousa Alves3Silva Seiça15da Silva Costa10Kliemaschewsk de Araújo6Martins Faria21Domínguez Encinas17Norton7Cantuário da Silva28Silva Sobrinho20LacasseThe formation 4-5-1 was formed.
12McLauchlan6Middag21Martinez2Docherty7Hay18Cornet24Kerr23MacLean15Arnot
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