Martinez, who led Wigan to the FA Cup last season, has signed a four-year contract to replace Manchester United-bound David Moyes.
Moyes led the Toffees to the Champions League just once during a much-lauded 11-year reign, but an ambitious Martinez is ready to plot the club's return to Europe's elite.
Toffees owner Bill Kenwright, who flanked Martinez at Wednesday's press conference, revealed one of the 39-year-old's first assurances was to take the club to the Champions League.
"When David (Moyes) 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'," said Kenwright.
"Almost Roberto's first words to me were 'I'll get you in the Champions League'."
Martinez denied that represented any immediate pressure on his shoulders, clarifying that any lofty ambitions would take time to realise.
Everton have been dwarfed by the spending power of their major Barclays Premier League rivals, and while Kenwright has pledged to back his new man in the transfer market, Martinez admitted he will have to be creative.
"The chairman hasn't put any pressure on me," he said.
"We have a very strong team and over the next few months we need to get together and make sure we are a winning side.
"Finishing in the top six was magnificent for Everton but we need to achieve more.
"There are six (Premier League) teams who are competing at a different financial level to the others.
"What is true is not always you need the money to achieve your aims.
"The aim for Everton should be to get into the Champions League. That doesn't mean next season but that has to be the aim for the future.
"It is not going to happen overnight. In football you need to be creative, find a way to be creative.
"We want to be involved in Europe and the Champions League, and we have to have the dream to fight for."
One of Martinez's first jobs will be to persuade the likes of Leighton Baines and Marouane Fellaini, both linked with summer moves away, to stay.
Kenwright insists no players have asked to leave and he is confident that will remain so.
And he also pledged to back his new manager financially.
"I'll give him a few quid to spend. The others are not for sale. We don't want them to go, they have worked massively hard for this club," he added.
"Roberto doesn't want them to go, he has all their numbers and he will be on the phone asking them not to go.
"Not one person has even half indicated they want to go.
"I am confident that squad, plus some Roberto signings, will form this club's squad for next season."
Martinez said he was ready to embrace the challenge of taking the club to the next level.
He left Wigan after four years which ended with him not only winning the FA Cup but also getting relegated.
"It is a real special day to come to Everton and have this feeling already of excitement and honour and I'd like to thank the chairman (Kenwright) for this opportunity," he said.
"There is huge pressure but I am extremely proud of that pressure because it means what David Moyes did in 11 years is set high standards and lay an incredible platform.
"I feel lucky to be able to carry on that work. He has given Everton an identity and an incredible standard and all I want to do is be humble and hard-working enough to take this magnificent job to the next level."
Asked why he had chosen now to leave Wigan, having turned down Aston Villa and Liverpool previously, he added: "It is simple: it came in a natural way.
"It has been a phenomenal time at Wigan but after four seasons this was the right time and I knew Everton was the right club.
"It has been a natural transition to be involved in such an exciting club."
Kenwright said he was pleased to get his man after a long search to replace Moyes.
"It was exactly four weeks ago today that David told me he wanted to become the new manager of Manchester United, and in that time the club has continued on a long and exhaustive journey to find the right man to take this club forward," he said.
"During the four weeks I have met some of the finest individuals you could meet in football, and the finest of them is sitting next to me know.
"It is a great relief, joy and seriously exciting for me that Roberto Martinez has agreed to be the next manager of Everton.
"To Evertonians, I say if you had been at the meetings and conversations I have had with your new manger, you will be as thrilled, excited and in awe as I have been."
Kenwright, who revealed he went to last month's FA Cup final to assess Martinez, was instantly impressed by the Spaniard.
"I'm not going to say to you it was like David Moyes, who got me in 30 seconds, he took at least 45 seconds," he added.
"He showed me how he beat Manchester City at Wembley. I'd gone there to look at Roberto.
"He understands the game and he understands Everton. When you know, you know.
"We did discuss at the first meeting we didn't want the standards and position David had achieved to slip: we wanted to build from that and that is the only statement we made.
"I have to play my part in it too. I don't want to be the man who asks him to come here and get Champions League unless I can support you.
"Myself and the board will be doing all we can to support Roberto."
Everton chief executive Robert Elstone was also delighted with the appointment.
"We have a top manager, we have an 'Everton' manager - which was important to us but I am also excited to give Roberto the support for what he needs to achieve," he said.
"Our objectives are all about what happens on the field. It is all directed towards Roberto."
Martinez has been linked with moves for some of his former players like midfielder James McCarthy and forwards Arouna Kone and ex-Toffees youth team prospect Callum McManaman.
"There is always a normal assumption that when a manager moves on he will bring those players along," said the new Toffees boss.
"It would be a big mistake to look at the manager's previous team.
"We have to look at the whole range, world football is a big market."