After being held to a draw by Amsterdam on Tuesday, the north London club still has a lot of work to do to get into the group stages of the competition.
The Dutch side claimed a 2-2 draw in the first leg of the second round of the playoffs after the Gunners had fought back from a goal down.
Stina Blackstenius struck just six minutes after Romee Leuchter's effort to give the visitors a lead.
The substitution thought she had won the game for the home team.
Rangers will have to overturn a 3-2 deficit to advance after they were beaten by Benfica at Ibrox.
Rangers, who are trying to reach the group stage for the first time, were involved in a game that ended in a 2-2 draw with Benfica.
The Portuguese side, who also hit the woodwork twice, won it on 79 minutes when Victoria Esson failed to keep a ball out of her net. Pauleta was credited with the win.
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