Strong results did not materialise.
The north London club were sixth in the WSL after winning just one of their opening four games, while they suffered a demoralising 5-2 defeat at Bayern Munich in the Champions League three days before that defeat at home to Chelsea, where some fans could be seen clamouring for his sacking by waving P45 signs.
So, on the Monday after that match, Eidevall informed the club of his intention to step down.
Asked whether the club were surprised, he says: "Yeah I think so."
Yet it ended up being a quick process, explains Eidevall, who had not told the club he wanted to leave the next day, but that's when his departure was announced.
"They were onboard with that decision \[to leave\], which very much told me that if the club is onboard with that decision it's 100% the right decision to walk away," he adds.
"So that gave me that little bit extra sense of clarity in where we were at."
With time to reflect on his departure, he looks back on his spell in north London fondly, focusing on the "immense growth" the team went through off the pitch.
"Both my mission - and also the club's - was to make sure that Arsenal was back to the top of the women's game," he says.
"I think you can argue on a lot of levels right now Arsenal are that, with having the Emirates as the main home, having really, really good attendances both home and away, having much-improved facilities and staffing around the team, and having a team that has a better mix of youth and more experienced players.
"That part is really good, and I can see my part that I played in that."
On the pitch, he says that "you can argue quite fairly" that Arsenal were the second-best team in the UK behind Chelsea during his time as manager, if you take all the competitions into account.
"When you see the resources - with player salaries and other costs around the team - Chelsea are by far the biggest spender and it reasonable that they are also the best team," Eidevall says.
"To be above \[Manchester\] City and below Chelsea is probably a reasonable result to get from what was invested.
"Would I have liked to get a league title? Yes, very much. Then I would have been very, very happy with the results."