The 39-year-old led the Latics to their first ever major trophy with victory over Manchester City in this season’s FA Cup final, only to then suffer the agony of relegation to the Championship.
Some believe that this questionable Premier League record makes him the wrong candidate to build on his predecessor’s solid 10-year spell at Goodison Park, but Martinez is unfazed by such speculation.
|2/1||Roberto Martinez is 2/1 with William Hill to spend four or more years at Everton
"It is something which keeps you desperate to see what you can do and one day turn them around so they are happy with the work you've done.
"I need to answer all the critics with work and that is nothing different to what I've done in the past. The only thing I want is for every fan at Everton to be proud of what we are trying to do."
The Spaniard is very excited the strength of the squad left in place by the previous regime, and hopes to build on those foundations by adding extra quality to the team.
"We can't lose the good things that Everton had last season," he continued. "If you look from a football point of view they were the strongest team at home," he added. "I am very fortunate to have the players Everton has at the moment. It is an incredible starting point.
"The Everton team last season never really showed a weakness. What you want to bring is an extra dimension and extra competition for places.
"The players know how to always be in games, they always know how to compete and that is something we can't lose next season. But we need to bring in some new signings, develop that competition and give us different options on the field.
"Slowly we need to bring a couple of players who can help the players in the dressing room. It is a natural transition and the right time to do it is in pre-season, we need to work on many aspects but more important we don't lose the phenomenal things they did last season.
"In any club you want to go from window to window having a stronger side and that is what we will have to work hard to make sure we don't let this group of players down."
Martinez became synonymous with a possession-based game during his tenure at the DW Stadium, and there are some question marks over how he will implement this style of play at his new club.
However, the former Wigan boss is adamant that he will not try to change too much too soon, and has confidence in his new players' ability to adapt.
"The players in the dressing room are internationals, they can work on certain aspects and we can always work on other areas," he explained. There is a big difference between the style and the system you play.
"I think the style will be similar to what Everton's has been over the last few seasons. Then on top of that we need to try to develop other ways of playing. We will work on that and make sure we have that flexibility."