The Toffees' 3-2 loss at Newcastle on Sunday was their fifth in seven Barclays Premier League games and their third defeat in a row.
Martinez insisted afterwards that Papiss Cisse should have been sent off for an elbow on Everton's Seamus Coleman in the first half - an incident referee Craig Pawson took no action over, and was shortly followed by the Magpies striker drawing the scores level at 1-1.
However, Martinez also had no doubt his team had made life difficult for themselves with their defending - something for which they have often been criticised this season.
And the Spaniard said: "We can't feel sorry for ourselves - we need to make sure that we get better in what we do.
"(For Newcastle's second and third goal) we gave the ball away when we should have been a bit more cute, showing a bit more maturity.
"I know we have got young players in the squad, but it's an opportunity to learn from those moments.
"We can't just keep giving cheap goals away in that respect because it becomes a harder game."
Martinez was disappointed for Arouna Kone when the Ivory Coast frontman ended up on the losing side at St James' Park after scoring his maiden goal as an Everton player.
Kone, whose spell with the Merseysiders since joining them in the summer of 2013 has been blighted by a long-term knee injury suffered in October that year, netted five minutes into what was his first Premier League start for the club.
Martinez said: "You can see what he brings - he's a completely different striker to the others we have at the club.
"He holds the ball up, he gives you a real platform, his intensity in the box to get on the end of crosses is very, very good and to get a goal so early coming back after a long absence is very pleasing.
"It's a reward that he deserves
It's just a shame that he couldn't celebrate a good victory with it."
Martinez - whose team are 12th and next face Hull away on New Year's Day - saw the Toffees fall 3-1 behind after Cisse's equaliser through goals from Ayoze Perez and Jack Colback before Kevin Mirallas' late reply.
The visitors lost influential midfielder James McCarthy, who has been troubled by hamstring problems, at half-time in the contest.
"It was more a precaution," Martinez said.
"James came back from injury on Friday and he was able to play 60 minutes, and after half-time he was hitting a very high risk of injury, so he had to come off."
Source : PA
Source: PA