Arsenal also struggled to draw 1-1 against Juventus in their Champions League clash in Turin.
The Gunners, missing a number of players including the injured England international Beth Mead, fell behind early in the second half when Lineth Beerensteyn put Juventus in front following a quick counter-attack.
Vivianne Miedma headed in from a corner just after the hour mark, but Jonas Eidevall’s side couldn’t produce a late winner.
Arsenal, who want to increase their start by 100 percent, are at the top of Group C, two points ahead of Juventus and three of Lyon, who won 3-0 in Zurich.
The Gunners got off to a good start, with Miedma leading the attack while Mead is expected to be sidelined for a long time after rupturing his anterior cruciate ligament in Saturday’s Women’s Super League defeat against Manchester United.
Stina Blackstenius was played by Frida Maanum, but saw her shoot over the crossbar.
Juve goalkeeper Pauline Peyraud-Magnin, who has had several spells with the Gunners, made a brilliant save after Sweden’s Blackstenius’ shot was well redirected before the break. At the other end, Arianna Caruso put the ball in the first quarter.
Arsenal pressed ahead early in the second half when Australia’s Caitlin Food tested Peyraud-Magnin before Lotte Wubben-Moy’s header was cleared off the line.
But it was Juve who broke the deadlock in the 51st minute when Dutch forward Beerensteyn blasted over Arsenal midfielder Manuela Zinsberger.
Arsenal responded to equalize just after the hour when Miedma headed in a corner. Miedema sent in another shot on the turn and in stoppage time almost put Food on goal, but the Juventus defense held firm.
Arsenal’s next game is the week after the next when they will receive Everton on December 3 in the Women’s Super League, starting at 2pm.
The Gunners’ next Champions League game is the return leg against Juventus at the Emirates Stadium, kicking off at 8pm.