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.
Martinez was unable to watch it live because Everton were playing Real Betis, but recorded it and admitted he feels a similar way about the Latics to a fan.
He said: "I love watching football full stop. I thought it was a good game. They are big events, every time that you play for a trophy.
"You always follow former clubs with a special feeling and you want them to do well. You can't be too neutral. And when they do well you feel part of it, the same as a fan."
While success at the DW Stadium was staying in the Premier League, the demands at Goodison Park are much higher, although financially Everton cannot compete with the biggest clubs.
Martinez thinks his experiences at Wigan will stand him in good stead, saying: "It doesn't matter if you're fighting to get a top position in the table or to avoid relegation, every game matters, so it's not a real different feeling.
"But embracing the challenge of being at a big club like Everton in terms of the expectations, understanding the responsibility and the history that we bring with our name, that is a very exciting part of the position that I'm in."
Martinez signed three players who were with him at Wigan last season, and goalkeeper Joel Robles and striker Arouna Kone should be in the squad tomorrow but defender Antolin Alcaraz is sidelined with a hamstring problem.
Winger Magaye Gueye and full-back Tony Hibbert are also out, although the latter is set to resume training on Monday, while midfielder Darron Gibson is 50/50 after straining a knee ligament against Betis.
Martinez is excited to get stuck into the season proper, although he is disappointed his first match will not be at home.
He praised the summer recruitment of Norwich boss Chris Hughton, who has added Gary Hooper, former Everton target Leroy Fer, Martin Olsson, Nathan Redmond and Ricky van Wolfswinkel to his squad.
Martinez said: "You always hope for a home start. That allows you to settle in and straight away you want to be comfortable playing at home. As it is we've got a difficult game at Carrow Road.
"I do feel this Norwich side probably is the best that's it's been in the Premier League. They've kept a very good core of players but they added really well. We do expect a really tough fixture."