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With Beth Mead and Vivianne Miedema both sidelined by ACL injuries, Eidevall had last month expressed his desire for a "prolific goalscorer" to be signed.
On Monday, the Gunners had a world-record bid of £500,000 for forward Alessia Russo rejected by Manchester United.
Sky Sports News understands Arsenal offered various forwards and cash deals for the 23-year-old during negotiations with United.
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One of the players Arsenal offered was Stina Blackstenius, who is the club's presumed starting striker for the rest of the season. However, United later informed the north London club they had decided against selling Russo.
Reflecting on the January window, Eidevall said: "I think I was clear in the window that we needed another forward and we identified targets.
"I know the club worked very hard, but it was a very difficult transfer window, not to find players to want to play for Arsenal, (and) there is plenty of high quality, but to find clubs wanting to sell quality players.
"That was very tricky and we were not successful, and of course we are disappointed with that, but now we have to look forward and make the best of the situation. I still have a squad with a lot of qualities, that I believe a lot in.
"We are short in numbers, we know that, that can be a potential problem, but we have to work together and do it as good as possible to reach our goals.
"Without going into details on discussing what our targets were, we searched globally for players. It was a very tricky window to find clubs wanting to release players because it's an immature transfer market where if they release a player, they have a really hard time finding their replacement.
"We knew it was going to be hard, but it was even harder than we thought."
However, Arsenal - who are currently third in the WSL - did have a busy window. Midfielders Victoria Pelova and Kathrine Kuhl, plus goalkeeper Sabrina D'Angelo were signed, while teenage Brazil winger Gio was recalled from her loan spell at Everton.
But Eidevall believes Arsenal are still short on players - likely referring to forward areas - and says he will now focus on getting results with his team.
Eidevall told a press conference on Friday: "I think recruitment is key if you're going to be a successful team.
"Last summer I think we got one player too little, and now we did that again in January. So obviously there are things we need to look at in order to be better because over time these things really have a big impact on the way we can perform and ambitions we need to have. That's very important for us.
"You can have results, or excuses, I don't think you can have both, and I am going to try to have results."
Hayes happy with Chelsea squad: 'I prefer to do business in June'
Elsewhere, Chelsea manager Emma Hayes says she is happy with the squad she has, having not signed any new players in January.
She said: "Our decision not to add to the squad this window was because strategically we always prefer to do our business in June.
"January is a notoriously difficult window in men and women's football. That was proven the case in this one. We are happy with our squad as it stands. I much prefer to focus on June windows."
Two of Chelsea's star players - Pernille Harder and Magda Eriksson - both see their contracts expire this summer, but Hayes did not give anything away when asked if they could extend their stays.
"Discussing players and their current situations and links to clubs is not a place for this forum," she said.
"It's between me and the players, and the club and the players. Everybody knows they're in the last six months of their contract, so yes, that's a possibility."
How the January window changed WSL transfers forever
The January transfer window was another watershed moment for the WSL.
There were record bids for Alessia Russo and a British record move for Bethany England, plus Aston Villa and Tottenham proved their mettle in the transfer market.
There are also questions to be asked to - is this the last window before we see a million pound women's player? And which players will use their transfer to stake a World Cup claim?