The Gunners host Aston Villa at Meadow Park on Saturday (2.30pm) looking to hold onto third place, having lost 2-0 at Chelsea last weekend.
They have a three-point cushion over Manchester City and superior goal difference of plus-11 and Eidevall says they will leave no stone unturned.
“It’s an important game. We need to recover, refresh and then be ready to go against Villa. We’ll leave everything on the pitch,” he told arsenal.com.
“Our aim is to finish as high as possible in the table. Most realistically, that’s going to be third place.
“Let’s bring it all on Saturday. Let’s do our very best. Let’s try and finish the season on a high.”
Having won 4-1 at Everton last Wednesday, with a brace for Caitlin Foord and other first-half goals from Katie McCabe and Lotte Wubben-Moy, Arsenal fell behind midway through the first half against Chelsea on Sunday, as Guro Reiten struck.
Magdalena Eriksson doubled the home side’s advantage just before the break, but Arsenal improved after the restart only to see McCabe miss a penalty and Foord hit the crossbar.
“We got off to a slow start. Chelsea are very aggressive in their pressing. We were prepared for that, but we did not find enough equality to play our way out of their pressure, which led to them building a lot of momentum in the first half,” added Eidevall.
“What I’m proud of is that we managed to turn that around. We improved our quality, we found our way back into the game, and we started moving the ball better and faster.
“We were not efficient enough with our goalscoring opportunities. If we had converted one of those really clear opportunities, penalty included, I think we could really have changed the game from a result perspective as well.
“We need to convert and that’s disappointing of course, but I’m still proud of the players for the way that they stuck with it and the way they turned the game around from a performance perspective.”
Arsenal were cheered on by a large group of travelling supporters in a crowd of 3,456 at Kingsmeadow and Eidevall thanked them for encouraging the squad through thick and thin this season.
“It’s hard to put into words, but it’s part of what’s made this season special,” he added.
“It’s part of making the future bright. So keep on being loud. Keep on being supportive. We love it.”
Arsenal defender Jen Beattie is also looking for a big finish on home soil.
“It’s nice to play at home on the last game of the season,” said the Scotland international.
“We’ll have our home crowd there and hopefully, it’s a good occasion, we’ll get three points and we’ll get Champions League.
“It’s been a very up-and-down season. To win a trophy [Conti Cup] was incredible. To have so many injuries was the exact opposite. But hopefully, we can finish strong.”
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