For weeks now Roberto Martínez has been preaching the need for positivity and for players and fans to "remain focused" as results on the pitch go south. And the Wigan manager was at it again in his programme notes saying: "We mustn't allow the negative talk or comments from people away from Wigan Athletic to distract our focus and desire for perfection in every performance."

Forget perfection, what football folk in this pie-and-rugby league stronghold require is what Martínez called "the only cure to our heartache": three points.

His band never got them here, failing to add to their paltry three league wins all season, though they appeared to have mugged Everton after 76 minutes when a Phil Neville own goal from Jean Beausejour's ball gave Wigan an undeserved lead.

"It was a complete fluke, freak, whatever you want to call it," was David Moyes' correct description of the way the ball somehow spun beyond Tim Howard. He was also correct to add: "I didn't think we looked like we were going to concede a goal."

For Martínez a point was better than nothing. "We haven't had much luck this season, it was welcome to have that break," he said of his team's opener. "I thought it was what we deserved after the dominance that we had and the attacking threat that we showed and the real intent to try to play our football in difficult conditions. At that time it looked like it was the right reward and that it was going to be our day but unfortunately it wasn't."

Of Everton's equaliser Martínez said: "I don't think they came strong, I think they just tried to be direct as they did all the game. We were never outplayed, we were never opened up and it was unfortunate in the second phase of a dead ball situation where they found the back of the net."

Thrown on in direct response to losing the lead, Victor Anichebe fashioned a fine header from a Leighton Baines cross after his corner was served back to him. Before this, the game had been a catalogue of technical mishaps and bad shooting. Darron Gibson is one of those players often described in dispatches as "having a shot on him" — as he proved with the 25-yarder that defeated Manchester City last time out — but in the first half an similar long-range attempt was so awful it went for a throw-in.

Jordi Gómez tried to show him better with a 28th-minute free-kick but his left foot only spooned it high. Steven Pienaar, back on-loan to Everton from Tottenham Hotspur, was next up but his awkward right-foot effort from the edge of Wigan's area lacked power and belief.

When Baines decided to end this finishing deficit by launching a Hail Mary that came down on Marouane Fellaini's head six yards from Ali al-Habsi, the first goal finally seemed incoming. But the Belgian stooped, headed it backwards and the ball bounced to safety.

To close this first-half show of misdemeanours it was fitting that Gibson finished what he started – stepping up to blast over from close range to send the sides into the break needing to reach for inspiration.

When Victor Moses made a bright break and swept the ball across and into Gómez, hopes lifted of the first strike and a quality increase but the forward's aimless pass illustrated precisely why Martínez's team are stuck to the bottom.

Nikita Jelavic came on for his Everton debut but his first touch was a mistimed control, which was apt.

As Martínez says, they need to start winning. The last Wigan home victory was on 25 September when the Catalan Dragons lost to the Warriors. Martínez's troops have not offered up a three-pointer here since 27 August when QPR became their first and so far only home victims.