Naismith spent five years at Ibrox before moving to the Toffees in the summer when he opted against transferring his contract from the Rangers oldco to newco.
But the 26-year-old admits he always enjoyed the intensity of life at Rangers, where every game was viewed as a must-win contest.
"I liked how standards or expectations were that high that there was no hiding place. Any time you drop points at Rangers it's a bad result," Naismith told the Daily Record.
"I liked the intensity of being an Old Firm player. The expectation was so high and there was no hiding place.
"Any game you don't win, it's a bad result. You needed to win every game. I liked that there was no hiding place - it made you a better player.
"You are never going to change that. A lot of things will need to happen for that to change. But I grew up around about Glasgow, supporting one half of the Old Firm. It was the norm for me."
Naismith believes there is not as much pressure to win at Everton, although he insists manager David Moyes still holds his players to high standards.
He added: "In a way at Everton there isn't as much intensity and scrutiny as Rangers but the expectation is still there and that comes from the manager.
"We want to finish in the top four and there is an expectation when you play. But if we go away to play Manchester United or City and get a draw, it's a decent result. That's where it differs from Rangers."
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