Saturday's trip to face Norwich at Carrow Road will be the Toffees' first competitive match for more than 11 years without David Moyes at the helm.
Martinez has been hugely complimentary about the job done by now Manchester United boss Moyes and his team, but he is keen to put his stamp on the club.
The Spaniard knows the luxury of time is something rarely afforded to football managers, but he hopes Everton supporters will see what he is trying to achieve.
Martinez said: "Any period where you want to change things, that's going to take a little bit of time. I'm trying to get to know what the fans want and look through the DNA of Everton, and that's important for me.
"I think we are very good at things but to achieve things you need to be outstanding at something and that takes time. When you're trying to take that next step, the changes need to be difficult to achieve, otherwise you will never get the benefit.
"It's just having the patience and the togetherness of understanding the period we're going through, but at the same time being able to enjoy it and making sure we're still competitive and winning football games while that happens."
Whatever happens at Goodison Park this season, it is unlikely Martinez will experience the same extremes of emotion as during his final campaign at Wigan.
Three days after leading the club he used to play for to FA Cup glory, Martinez watched on as they were relegated following defeat to Arsenal.
Wigan, now managed by Owen Coyle, were back at Wembley last Sunday for the Community Shield, which they lost 2-0 against Manchester United.