The Scotland striker netted the only goal of the game in Saturday's 1-0 victory over Chelsea - Everton's first win of the season after three successive draws.
Naismith scored four goals in 35 appearances under David Moyes last season following his move from Rangers, and he hopes to vastly improve that tally this term.
"Last season was my first season back from a knee injury, which takes time, plus it was my first season back at a new club which takes time," said Naismith, who made his first league start of the season against Chelsea.
"At previous clubs I've taken time to settle so hopefully this can be the start.
"It was unfortunate for Steven Pienaar to be injured but it opened up the door for me to get my chance and hopefully I can carry that on and get selected again.
"You have to earn your place. When you come to a club like Everton and you are competing for European football, you expect the quality to be high and for there to be competition for places.
"I am up for the fight and I wouldn't have come here if I wasn't. I'm glad to be part of this squad and I hope to be able to contribute more."
Naismith also believes new manager Roberto Martinez has installed an air of confidence in the Everton squad since he took over the reins from Moyes.
"We feel we can compete against any team we come up against and we have shown that in the first few games where we've played really well without getting the results we wanted," added Naismith.
"It has been a big change from the previous manager in terms of the style we are playing and that will take a bit of getting used to but we have shown we can carry out what he wants and cause trouble to the best of them.
"It gives you a bit more freedom because the manager wants you to go and express yourself going forward."