Martinez's side are bottom of the Barclays Premier League and surrendered two vital points as Everton hit back to claim a 1-1 draw at the DW Stadium last week.
But the Spaniard was pleased enough with the performance, after four successive league defeats, to approach the remainder of the campaign with confidence.
Latics are five points adrift of 17th-placed Wolves ahead of Saturday's vital clash against neighbours and relegation rivals Bolton at the Reebok Stadium.
Martinez said: "At the end of the game you always feel like you have dropped two points, especially when you score that first goal and have an opportunity to score the second.
"But overall I felt we played really well. We were back to ourselves, we controlled the game and made it very difficult for Everton.
"They are always a very competitive side, one of the most hard-working in the league and I felt we played really well.
"For me that was a real change in level of performance. We were not happy with the levels we showed at Spurs and QPR.
"I think it is important we find a very consistent level between now and the end of the season.
"I do feel that was a real turning point for us going into the last third of the campaign."
Martinez is well aware Saturday's encounter is likely to be a tense affair.
The two clubs - these days less than eight miles apart following their moves to modern stadia - have enjoyed a fierce local rivalry for decades and this year the stakes are high.
Bolton are only four points better off than Latics in the fight to avoid the drop and, with 14 games left, the margins for error are narrowing.
Martinez said: "We are looking at our home games and feeling we have to win every single one of them. It is going to be the same for Bolton.
"It is a big derby for ourselves. It is always a special game but now this season, with both clubs fighting to avoid relegation, it has got an extra meaning.
"But we know we have to reach a very good level in all the next 14 games.
"It is no good to go to Bolton and get a fantastic result and then have three bad performances.
"We can't get in any worse position in the table - everything is in front of us to be achieved, but we are ready for that.
"We have difficult games but we are really excited about the challenge.
"We are desperate to be successful."
Martinez continues to draw encouragement from last season's last-gasp escape from the drop.
Latics survived last May after a dramatic 1-0 win at Stoke on the final day.
The Spaniard said: "The real advantage we have got is that we have been through this situation many times before as a football club and, as a squad, we did it last season.
"We know what we have to go through and how we have to perform.
"We are going to have a big following at the Reebok and from now until the end of the season they are big cup finals."
Defender Antolin Alcaraz and midfielder Mohamed Diame could return to the Wigan starting line-up after injury and international duty respectively.
Martinez is also expecting new signing Jean Beausejour, the Chile winger signed from Birmingham last month, to make a big impression on the squad.
He said: "I have been a huge admirer of Jean for many years, the way he has been playing for Chile. He brings great penetration.
"The manner he has played in the last two games, it seems he has been working with us for months.
"I think that is a real sign of the intelligence and footballing mentality he has got.
"As a character, he is the typical Wigan Athletic personality that we want in our squad."
Wigan are expecting to take a large following to the game with many fans walking to the ground to raise money for four-year-old local girl Emma Hoolin, who is receiving treatment for cancer.
Martinez said: "Little Emma is one of those great initiatives that reflects a lot about our football club. It makes you extremely proud of Wigan Athletic."