The Goodison Park club finished fifth in the Premier League last term following an encouraging first campaign under Martinez, adding to their squad over the summer with permanent deals for Romelu Lukaku and Gareth Barry.
And although the likes of Manchester United - seventh last term - Chelsea, Arsenal and Liverpool have all invested heavily during the close-season, Martinez is confident his club can break into the Premier League's top four.
"When I went to the World Cup, I sat down watching games and thought 'who here is better than what we have at our club?' And it was difficult," the Spaniard is quoted as saying by The Mirror.
"I think the Premier League this season will be quite unique because of the number of teams fighting to get into the top four.
"Manchester United will be a force, 100 per cent, the top four of last season [Manchester City, Liverpool, Chelsea and Arsenal] will be stronger and I think Spurs will benefit from all the investment of a year ago.
"But I would like to believe we will benefit from being together for 12 months and we will be stronger.
"I will never shy away from trying to get Champions League football because that has to be where we're trying to get to.
"When it's going to be, I don't know, but it shouldn't be down to just money to get into the top four positions."
Everton smashed their transfer record when agreeing a £28million deal for Lukaku last month, but have still spent less money than many of their rivals.
Nevertheless, Martinez added: "The real strength of this squad has been the continuity with signing Gareth Barry and new contracts for Ross Barkley and Seamus Coleman.
"And if I had millions and millions, I would have spent it on signing players such as John Stones and Ross.
"I'm in a very fortunate position. I would have spent millions on Gareth. I'm delighted with the players we have kept.
"Seeing Ross committing to a new contract shows how the chairman and the football club are working hard to give us a footballing future with financial solutions."