The Spaniard's era at Goodison Park was finally kick-started after three successive draws thanks to the confidence-boosting victory over Jose Mourinho's Chelsea.
However, Martinez knows that will go to waste if they cannot follow up with a good result at West Ham on Saturday and does not want his players to be lulled into a false sense of security after remaining undefeated through the first four matches of the season.
"It is vital (to build on the Chelsea victory)," he said.
"In any big win you need to give the value to those points with the next result.
"I do feel being unbeaten speaks volumes for the work-rate of the squad and of how well we have been focusing on each game.
"Now it is important we follow the victory over Chelsea with another good performance in a difficult environment at West Ham.
"We don't take that victory for granted and we also don't take being unbeaten for granted.
"It is that time of the season where we need to keep all the good things we have and keep working on the other aspects of the performance and we can be a good team if we do that."
Martinez on Thursday night watched the Wigan side with whom he won the FA Cup last season make their Europa League debut.
He insisted he was not envious, having missed out on that adventure, as he was hopeful of not only getting Everton back into Europe but competing for and winning trophies on the continent and at home.
"We are in a situation with the history we have at the club that we don't need to get any inspiration from elsewhere, we are looking internally," he said in references to the Latics' European debut.
"We have nine league titles and that is what we have to try to carry on working on to continue developing our history and make sure our fans can be very proud.
"We need to be competing to try to win titles and effectively be one of the best teams in the British game.
"Of course Everton (can get back to winning trophies). As a football club you have that in your DNA.
"You know you have done it in the past but you are realistic of the game now.
"There are six (Premier League) clubs who are existing in a different financial market.
"But that is where, in football, you have to be creative enough to be able to find a way to bridge that gap and be able to compete against anyone.
"It is not going to happen overnight, it's not going to happen this season but you need to be patient.
"What we showed on Saturday as a football club, with the chemistry between the players, staff and crowd, could help us to bridge that gap.
"I said after the game it is incredible the amount of ingredients any winning team has to have and we showed that in abundance.
"It was a fantastic experience to see how the next nine months of competition are going to develop and that is what we are going to use to our advantage.
"We have a fantastic base to work as hard as we can and the competition for places is really strong in every position, we have two or three options."