"I was disappointed not to start in the game against Watford but then you look at the boys who scored and done well and accept that and bide your time," he was quoted as saying by the Liverpool Echo.
"And last season, I felt I contributed a lot to the squad.
"The first year with a new manager you do need to prove yourself but I think I've done that and shown my worth to the team."
Naismith is well aware of the fact that he faces tough competition for a place up front with team mate Romelu Lukaku in fine form and scoring a brace in the club's 3-0 win over Southampton on Saturday.
"The boys who have been playing up front have been doing well," Naismith said. "It's down to me to work hard and wait for the opportunity to come.
"If I feel I've not been treated right then I will speak up but it's down to boys doing well and scoring goals, so you are not going to take those boys out of the side."
Naismith hopes team mate John Stones, who has been heavily linked with a move to champions Chelsea, will stay at the club.
"We definitely want him to stay -- he is a fantastic guy and footballer and a mainstay in our team," Naismith told Sky Sports about the defender. "You want your best players to be here to hopefully continue bringing success to Everton."
The former Rangers player has also been working on his coaching qualifications to see if he could take a crack at management after retirement.
"I'm doing my B-Licence at the moment but I wouldn't say I have a massive draw that I want to be a coach or a manager," Naismith said.
"I'm doing it more to get the experience to see if I do like it and if it's something I'd like to do."
(Reporting by Shravanth Vijayakumar in Bengaluru; editing by Sudipto Ganguly)
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