Norwich City's interest in Naismith was reported by the Mirror, who said the Scottish international was keen on a move, but Martinez blocked any transfer.
The Spanish boss claims that, despite a lack of first-team starts, Naismith remained too vital a player for him to lose, and he was not prepared to sanction any sale.
"Clearly, at that moment, we couldn't replace Steven Naismith," he said.
"It wasn't something that we could afford to do to lose such an important player like he is, even though he was finding himself not starting games."
Martinez will feel justified in his decision to keep Naismith at Goodison Park, after witnessing the hard-working forward's form so far this season.
The 29-year-old has already made seven appearances, and his latest one - in a 3-1 victory over Chelsea - was particularly impressive.
Naismith came off the substitutes' bench against the Blues and scored three times to become the first player to score a hat-trick against a Jose Mourinho side.
It was a win which pushed Everton up to seventh place in the Premier League table, with an away game against Swansea City representing their next assignment.