The London club hit the woodwork twice in Sweden as an inspired showing by Hacken goalkeeper Jennifer Falk also helped keep the visitors at bay.

Chelsea are third in the league phase table after four matches, one point behind defending champions and pacesetters Barcelona, although the perfect Catalans hold a game in hand.

However, several teams, including Lyon and Arsenal - both of whom are just a point behind Sonia Bompastor's side - could leapfrog them this matchday.

"It's a frustrating result," Blues boss Bompastor told UEFA.

"We came here with the ambition of winning the game... But tonight it didn't go that way. We need to learn from this."

Women's Super League champions Man City enjoyed a 4-1 success at Inter Milan to earn a first win in the league phase after drawing their first three outings.

A first-half Aoba Fujino brace cancelled out Elisa Bartoli's opener for the hosts by half-time.

Kerstin Casparij and Grace Clinton were on target after the break to send City up to seventh in the table.

Paris Saint-Germain fell to a first defeat as Bayern Munich held on to win 2-1 at the Parc des Princes and climb to second in the table, ahead of Chelsea on goal difference.

Klara Buehl's strike five minutes from half-time proved the winner as she added to PSG goalkeeper Katarzyna Kiedrzynek's early own goal to put the Bavarians in a comfortable position.

Paulina Dudek halved the deficit from the spot midway through the second period but Bayern held on. PSG lie in ninth place on five points.

In the Spanish capital, Real Madrid downed visitors Paris FC 3-0 thanks to three second-half strikes.

A first win of the league phase sent Pau Quesada's side eighth in the table on six points, while Paris FC lounge 16th on two points.

Arianna Caruso broke the deadlock in the 55th minute and Lineth Beerensteyn thumped home soon after.

Linda Caicedo made the points safe with nine minutes remaining as she finished smartly from Felicia Schroeder's reverse pass.

"It was really important to pick up the three points today because we hadn't won any of our first three games," Caruso said. "We have to try to finish among the top teams."

Roma held on to beat Swiss side Servette 2-1.

On Wednesday, eight-time winners Lyon are in action away to Juventus.