The last time Wigan Athletic won in front of their home fans four days of the summer transfer window remained and Neil Warnock had yet to fall out with Joey Barton.

Warnock's Queens Park Rangers were the 2-0 victims that day – 27 August – the first and so far only team to fall to Roberto Martínez's side at the DW Stadium this season. Nearly six months on, Warnock has been sacked (with Barton criticising his regime), and from Wigan's 12 home league outings that sole win has been joined by six defeats and five draws with the Spaniard conscious that this cast‑iron relegation form has to improve now.

After losing the chance here when Victor Anichebe's late header cancelled out Phil Neville's 76th-minute own-goal, Martínez was asked if he thought a home win could lead to the few that would lift Wigan off the bottom.

"Yes. The performance today will help us a lot," he said. "Winning gives everyone confidence and belief but what pleased me most was the manner in which we played against an Everton side which is in great form at the moment. I am pleased how we defended, how we got on the ball. We were the team which dominated today more than Everton and did most to get the three points."

This was an optimistic view of a disappointing encounter but with 14 matches remaining and five points from safety Martínez's only option is to keep smiling and hoping. Half of those games are at the DW Stadium and he said: "We are ready – we are ready for the next seven games and for everything that's going to be thrown at us. Performances like that will keep us up definitely, with the squad we have got.

"Today was a big day for us. Performances like today give us a real competitive edge to the squad. Sometimes your situation can affect your football. We are not a strong team, one who will play long balls, be direct and play percentage football. We need to play with a smile on our faces, an arrogance and a bravery and we did that today. That's how we have to carry on as well."

Leighton Baines, whose cross was converted by Anichebe, is a former Wigan left-back who helped the club to escape relegation with a final day 2-1 win at Sheffield United five years ago. He said of this crop's hopes of staying up: "They can get out of it. They have done it before and I was part of it myself. It can be done but it is going to be difficult. They have to be careful not to get themselves too far adrift. They have to stay within touching distance of the other sides and you can only do that if you start winning games."

Baines pointed to Everton's 11th position and how David Moyes adjusted their style this campaign to yield results: "Wigan generally seem to play pretty well but for whatever reason they are just not winning football matches. It is nobody else's job to decide what they should do but they keep trying to play the same way – you wonder, do they have to adapt a little bit and find a way to win games? We have had to do that, earlier on in the season we weren't getting any results and so we went back to basics a little bit and that helped us out."