Martinez's men have to play each of the clubs that finished in last term's top eight within their first 10 games of the new season.
It looks a daunting schedule, but the Spaniard is eager for Everton to get points on the board.
"Looking at the start of the season, probably the fixture list has not been too kind to us," said Martinez, who wants to make three more new signings before the end of the transfer window
"But we are going to take it as being able to face a very strong challenge
We need to make sure we are strong enough.
"It is about making sure that as a team we are successful and do a lot better than we did in the league last season.
"I think the experiences of the last campaign will help us immensely."
Last season was a disappointing one in the Premier League for Everton, with them only managing an 11th-placed finish a year on from Martinez having guided them to fifth in his first term in charge.
They also had a Europa League campaign to cope with in the 2014/15 campaign and picked up only six points and one victory from their first seven top flight games.
They finished stronger, winning six of their last 10 fixtures, and Martinez said: "Last season was very unique - playing in Europe and having the good feelings from the season before put us in a position where we wanted to win games straight away, and create a bit of momentum, but we never got it early on.
"We lost too many points, and psychologically it was really tough - being in Europe also had an affect from that point of view.
"But the second half of the season was completely different, and we need to start with that kind of momentum this time, rather than how we started the last campaign."
Asked whether he had set targets for the season, Martinez added: "No
I think the first 10 games will tell us a lot about where we are, and from that point on we will be able to set some."
Everton begin their campaign on Saturday by hosting newly-promoted Watford, who have acquired a new boss in Quique Sanchez Flores - also a Spaniard - and 10 new players over the summer so far.
It remains to be seen how well the group comes together, but Martinez feels the Hornets are a "very dangerous" outfit.
"I would not view Watford as the normal newly-promoted side," he said.
"From the manager to the amount of players they have brought in, with really strong experience at the highest level, this is a new group clearly but straight away you are going to see a team that know what they are trying to do.
"I think it is a team ready to compete in the Premier League.
"Flores has become a very experienced manager and I don't think he'll find the British game anything of a surprise to him.
"I see them as a very dangerous team that I think are going to bring something very different to this campaign."
Source : PA
Source: PA