The team's success last term was built from the foundation of a solid defensive unit which conceded the third fewest goals in the Premier League.
But Everton have already shipped 10 goals in three matches this season, including six against Chelsea, and they threw away leads three times in their first two matches.
Martinez insisted poor luck has largely contributed to their downfall, but admits they need to improve.
"It is easy to see we have been a little bit slack in our defensive duties and we have been punished too easily and conceded too many easy goals," he said.
"It has been one of those situations where everything that could have gone wrong in our box has gone wrong.
"There may have been a lack of defensive intensity and that is something we need to correct but I do see a team that has improved from last season, even though the results are not as good as they should have been.
"We conceded in the 85th minute against Leicester (in the opening match) when we had got ourselves ahead twice.
"The late goals we conceded against Arsenal (to concede a two-goal lead) is more of a feeling (of) maybe wanting to see the game out and developing a bit of fear of something to lose at that moment of the game had a big say.
"We are quite aware of what we have to improve but the margins are very small. There is no need for drastic revolution, it is more about having a real focus and increasing that defensive intensity in specific moments.
"We had 15 clean sheets last season. Maybe we got a bit relaxed knowing we were so good in that area and we got punished and that is something we need to put extra emphasis on."
Criticism has been directed at the veteran centre-back pairing of Phil Jagielka, 32, and Sylvain Distin, who will be 37 in December, but Martinez is keen to deflect any blame and dismissed concerns over their age.
"It has been a surprise because we haven't lost any personnel from that back five (including the goalkeeper) and there are more than 1,100 Premier League appearances between them," added Martinez.
"I don't think individual mistakes have cost us at all. Age is never a problem, experience is always a positive. When you have a player who cannot reach the level required it is not down to the age.
"Every player has different ages when the legs and energy levels start to go but that is not the case with any of our players at all.
"I feel for one reason or another sometimes we left ourselves a little bit exposed and we got punished, but it is not down to individual mistakes or players not being able to reach their level, it is a combination of aspects.
"Now it is all about small details. We can't wait to get back to the standards that we have defensively."