It is one of life's enduring questions: what would it take to shake Roberto Martínez's remarkable self-belief? No one could have complained if he had been in a bad mood after watching an untimely implosion from Everton, their spectacular show of self-destruction more or less ending their hopes of finishing in the top four, but that is not Martínez's style. And he is all about style.

Where other managers might have been brusque after such a calamitous defeat, Martínez was generous with his time, open with his answers and still, somehow, dripping with positivity, even though Arsenal will move four points clear of Everton with two matches left if they beat Newcastle United on Monday night.

Negativity is an emotion that Martínez does not appear to experience, each setback simply a chance to learn, develop and come back stronger next time, and it is not hard to see why players are so quick to buy into the Spaniard's philosophy. Rather than agonising over the farcical own-goals from Antolín Alcaraz and Seamus Coleman that gifted Southampton victory in the first half, Martínez was too busy enjoying life and being charming. It is easy to be suspicious of the eternal optimist, but that lack of cynicism is what allows Martínez's sides to push against glass ceilings.

"You're not involved in football to prove people wrong," he said. "I think you are involved in football to achieve dreams and set a good vision in a football club and I always felt that with the heritage and history we have, nine titles in our possession, we have to aim for Champions League football, and 69 points in another season, it would have been Champions League football.

"I'm excited about the players we have and the football we've played and today is a defeat we need to accept if we want to improve and get better. It's hurtful but I think it shows the standards and how much we've raised them when you get eight wins in 10 and feel really disappointed in the end of it."

For all Martínez's positivity, though, it is impossible to shake off the sense that Everton have thrown away a wonderful opportunity. They have won eight of their past 10 matches, hammering Arsenal and Manchester United at Goodison Park during that run, but losing to Crystal Palace and Southampton was not in the script. At this stage of the season, the best teams tend to find a way. They do not send diving headers into their own net in the first minute of a tricky game away from home.

"That's because of the perception of the opposition," Martínez argued. "You need to earn that. When you meet one of the top four teams sometimes you give them the draw and they don't have to play well to get a positive result. You want to get into the position where sometimes you can get that kind of respect but that's a process, you need to win those games first to develop that perception and respect and I think it's part of this magnificent league. The Premier League is the best league because of those reasons."

Everton's Seamus Coleman (centre) heads the ball past his goalkeeper Tim Howard to gift Southampton a second own-goal of the game. Photograph: Chris Ison/PA

If there is one question-mark over Martínez, it is in his ability to build a defence solid enough to challenge at the top of the league. Martínez inherited an excellent back four from David Moyes but without the injured Sylvain Distin and Phil Jagielka, Alcaraz and John Stones struggled.

That is one area of concern. Another is the size of Everton's squad. A long injury list forced them to name a 16-year-old, Ryan Ledson, on the bench, and Martínez wants fresh blood. They are restricted by their finances and Gareth Barry, Romelu Lukaku and Gerard Deulofeu will return to their parent clubs, but Martínez has plans for the summer. "Every summer is busy, we signed 10 players in the previous two windows and that's what you expect from window to window," he said. "I never worry about losing players. It's the opposite, I get excited about bringing new players in. You need fresh blood. We've got incredible senior players at this club, you've got Tim Howard, James McCarthy, Phil Jagielka, Leighton Baines, Leon Osman, James McCarthy, those players hold the dressing room together."

If it is to be the Europa League for Everton, then Martínez would embrace it. "European football would be a phenomenal experience," he said. "When you're playing in Europe you need to have another six or seven and we will do that. It's not an issue."

Man of the match Nathaniel Clyne (Southampton)