The Gunners pressed for long spells but were stung by goals from striker Conny Pohlers and left winger Martina Muller, both against the run of play.
Boss Shelley Kerr was not satisfied with her team's performance.
"Wolfsburg are a strong, physical team and we didn't match them," she said.
"We created three or four good chances, and if we had got a goal that could have changed the picture.
"But we can play better than that and it's a big ask now to get the goals we need.
"But this team has shown in the past that they can score away from home, and we'll go into the second leg believing we can get through to the final."