The Spaniard signed a four-year contract to take over from Manchester United-bound David Moyes, and outlined his plans to break into the top four at an upbeat introductory press conference.
Chairman Bill Kenwright said: "When David first came to see me, he sat down 11 years ago and we were in a bad state, and he said: 'We're not going down'. Almost Roberto's first words to me were: 'I'll get you in the Champions League'."
Martinez added: "It is a bit more of a long-term ambition of the club."
"Everton has an incredible history and tradition and the work David Moyes has done has laid a platform where, in the next few years, we should be dreaming of getting to the Champions League.
"There are six clubs (Manchester United, Manchester City, Chelsea, Arsenal, Tottenham and Liverpool) who are working at a different finance level to the others but I believe with our tools and our genetic make-up in the club we can find a way to compete with those teams.
"That has to be the aim for the future. It doesn't mean next season, in two seasons' time - it has to be the dream of every Evertonian.
"Where we are now is making sure we are really strong and carry on the work David Moyes did over the last 11 years, making sure we don't drop those standards.
"I am not saying it is a realistic target, that has to be the dream.
"In any club you need to be moved by an ambition and in football if you don't have dreams you will never achieve anything.
"It is important we set that clearly without expecting that to be a target straightaway.
"What Everton achieved last season was incredible, they had no right to finish top six and for them to break into that top six speaks incredibly of the job David Moyes did."
Martinez moved to Goodison Park from Wigan after an eventful season that saw them win the FA Cup but get relegated.