Everton were beaten to fourth spot by Arsenal despite taking four points off Arsene Wenger's charges in a promising first campaign at the helm for Roberto Martinez.
And Naismith, who featured in 31 Premier League games last season, has backed Everton to go one better this time around, with the likes of Romelu Lukaku, Muhamed Besic and Gareth Barry having signed permanently at Goodison Park.
"We are up for the fight. With the signings we have made we are showing the ambition we have got," Naismith said in quotes reported by the Liverpool Echo.
"We came really close last season and were unlucky not to get into the top four."
Naismith recognises that Martinez will need to utilise the full depth of his squad in order to achieve that goal, which could mean some spells on the sidelines for the Scotland international.
But the 27-year-old is prepared to play whatever role is required of him.
"What the manager has made clear is that football is a squad game now," Naismith added.
"And every player needs to be ready when he calls on us because you are expected to deliver.
"The manager stresses this in our team meetings and says that this is a squad game.
"It took a while for me to get used to not playing regularly but the manager explained the situation.
"I may not be playing one game but I know I could be called upon for the next."
