Having rounded off 2015 almost perfectly by moving stealthily into the top four, Tottenham Hotspur go to Everton on Sunday strongly tipped for a Champions League place and perhaps even a tilt at the title. And why not? They have a progressive young manager making a name for himself, a proven goalscorer in good form and one of the brightest English midfield talents to emerge for several seasons.

It is not going unnoticed on Merseyside that Everton can tick all those boxes, too. Plus, in addition to Romelu Lukaku and Ross Barkley, the counterparts to Harry Kane and Dele Alli at Spurs, Goodison boasts John Stones, everyone’s idea of England’s first-choice centre-half for the foreseeable future. Everton, however, are not making designs on the Champions League. Everton are 11th.

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The bottom half of the table is not where one would expect to find a team with three £40m-rated players in their ranks, assuming Stones’s value has not been adversely affected by his team conceding seven goals in their last two home matches. Naturally, Roberto Martínez denies it – this is a manager seemingly incapable of harbouring a negative thought – but with a new takeover in the offing, this is no time to be slipping down the table.

Some Everton fans have never been convinced by the former Wigan manager, others have been pleasantly surprised but are beginning to lose their faith. Too many of the old failings from Martínez’s former club are beginning to resurface. Everton play attractive, adventurous football but too often lack a killer punch or a mean streak. They are frequently naive, drawing or even losing games when they have done enough to win. Defending is a problem, not only in terms of decision-making and application on the pitch but in terms of the manager’s ability to identify and rectify weaknesses. While no one is saying Everton will end up being relegated, for a club with lofty ambitions and highly coveted players this is turning out to be another season of underachievement. Martínez might have to repeat his cup-winning trick from his Wigan days to win over all his critics.

With disarming frankness, Martínez accepts most of these charges. “As Everton manager, I take responsibility; we have to be a winning team,” he says. “We should be winning games and winning titles, not just looking to compete and hope for a win. Winning is in this club’s DNA and it has been too long since we won a title. We have the talent at this club: we are not quite the finished article yet, otherwise we would be top of the league, but we have to try to win something in the next five months.”

That is quite a call from the manager of a club who have not won anything for 20 years but Martínez is shrewd enough to know that Everton might not always have players of the calibre of Lukaku, Barkley, Stones and Gerard Deulofeu at their disposal.

The club manfully resisted Chelsea’s overtures to Stones last summer and will arguably be in an even stronger position to do the same again once the extra television income has been banked, although this is not simply a matter of money. All the above players know they could be playing at Champions League level, an aspiration that once again seems likely to pass by Goodison. Winning the FA Cup or the Capital One Cup would not necessarily plug that hole, although winning something would be a positive statement that might buy the club some time. As long as the trophy cupboard remains bare, Everton will always be at the mercy of clubs with deeper pockets and more impressive fixture lists because players want to test themselves at a higher level and are not generally in the habit of turning down better offers.

Lukaku cannot enjoy being the leading scorer if his goals are not proving enough to win matches, he has spoken before of his desire to play at a big club and is beginning to sound a little fed up in his post-match interviews. Everton’s fighting stance over Stones could not quite hide the fact that the defender fancied the move. Much more underachievement and Everton’s best players will be off.

Facebook Twitter Pinterest Everton resisted attempts by Chelsea to sign John Stones last summer. Photograph: Ian MacNicol/Getty Images

Martínez insists the overall plan is to improve the squad at every transfer window but his best chance of doing that is to win something with this one first – or break into the top four and hope that will keep it together a while longer.

“We have the opportunity with this team to be something special in the history of Everton, our attacking play is exceptional,” Martínez says. “We need to be better defensively, there are no two ways about it, but we have two experienced defenders coming back in Leighton Baines and Phil Jagielka.

“We have conceded too many goals and we can’t blame anyone but ourselves, but we have a pivotal month coming up and hopefully we can build up some momentum for the second half of the season.”

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That starts on Sunday – and for a manager who saw his side lose their last two home games, the pressure is on against high-flying Tottenham.

“If I am under scrutiny I happily accept it,” Martínez says calmly. “The Everton manager should be under scrutiny. That’s not pressure, that’s the nature of the job. I don’t want just to go through the motions, I want to be in charge of an Everton team that wins things. This job brings a certain responsibility, considering the club’s history, and I am looking forward to the challenge of the next five months. We should be higher, there is no doubt about that. But for our own mistakes, allowing teams back into games, we could have been around fifth, quite close to Spurs.

“There is no point looking back, we now play everyone else again and we simply have to do better. We have to fulfil our potential, to show what we can do. I think we have enough talent and character in the team to recover.”