City travel to Goodison Park on Saturday hoping for three points as they look to strengthen their bid for the Premier League title after Liverpool's loss to Chelsea last week.
Meanwhile, Arsenal will want Naismith and his team-mates to lose, as that would assure the London club of finishing in the final UEFA Champions League qualification spot.
Fifth-placed Everton currently sit four points behind Arsenal with two games remaining, but Naismith has vowed that Roberto Martinez's men will do everything in their power to finish fourth.
"It's disappointing that (it seems) we have missed out on that (finishing fourth) because, although it's not mathematically impossible, we slipped up against Crystal Palace and at the weekend (versus Southampton)," the Scot told the Liverpool Echo.
"We will definitely be doing all we can but Arsenal have capitalised.
"We will fight to the end but the main thing is that we have got to finish fifth."
Tottenham are a further three points behind Everton, and Naismith went on to say the Goodison Park club have their eyes on the UEFA Europa League should their bid for Champions League qualification fall short.
"All we are concentrating on is securing European football," he added.
"We would be so disappointed if we couldn't finish in fifth. I think we have deserved it for the way we have played this season and the push we have had for fourth."
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