The Merseysiders had enough chances to win, including four good ones in one crazy 60-second spell, but those unhappy supporters could not hide their frustration as Everton trooped off just two points off the relegation zone.
The missed opportunities were shared between Tim Cahill, who hit a post, Marouane Fellaini, Seamus Coleman, Steven Pienaar and Louis Saha, but a downbeat Moyes also took some of the responsibility himself.
No way through: Everton keeper Tim Howard bravely stops Wigan's Colombian striker Hugo Rodallega
Moyes said: 'I tried freshening things up in the second half and I thought we were a poorer team. My decisions as a manager were poor today and I have to look at that.
'The worrying thing is we are not beating the teams at Goodison Park we have done in previous seasons. I'mlooking to see if there is any reason for it beyond simply not taking our chances.
'Today, I couldn't see any. You don'tget better chances in the Premier League than we did today. They were shared around among different players and nobody converted any of them.'
Opponents Wigan are still in the bottom three but, given that they shipped nine goals at Spurs a year ago, a clean sheet at Goodison is not to be sniffed at. And they could have won it in injury-time when Tim Howard pulled off a great save to deny Ronnie Stam.
Midfield tussle: Wigan's Charles N'Zogbia battles it out with Everton's Jack Rodwell
Wigan manager Roberto Martinez said: 'We are more alert and concentrate better. We matched Everton's great intensity levels and finished the stronger side. It shows the progress we've made since that Spurs game.'
Everton barely average more than a goal a game at home and you could see why in the first half when Fellaini and Jack Rodwell missed close-range headers and Cahill allowed Wigan skipper Antolin Alcaraz to put him off a final shot.
Resilient: Mohamed Diame (left) was one of many Wigan players who put in a solid defensive display
No longer are Wigan the nice little club who roll over for the big guns. Hendry Thomas and Pienaar were involved in a physical tussle after which both were lucky to escape red cards.
MATCH FACTS EVERTON: Howard; Neville, Jagielka, Distin, Baines;Coleman, Fellaini, Rodwell, Pienaar(Anichebe 66); Saha (Beckford 60), Cahill.Subs (not used): Mucha, Bilyaletdinov,Osman, Yakubu, Duffy. Booked: Neville, Pienaar
WIGAN: Al Habsi; Gohouri, Alcaraz, S Caldwell,Figueroa; Cleverley (Stam 46), Thomas(McArthur 64), Watson, Diame, N'Zogbia;Rodallega. Subs (not used): Pollitt, GCaldwell, Boselli, Gomez, McManaman.Booked: Thomas, Gohouri, Figueroa, N'Zogbia
REFEREE: M Oliver (Northumberland).
'I thought the referee was consistentbecause both players could have gone,' said Martinez.
Everton could have guessed after an incredible passage of play in the 59th minute that it was not going to be their day. Pienaar played through Saha, whose shot was smothered by Ali Al Habsi.
In the very next attack, Cahill headed a Leighton Baines cross against the post and as Wigan failed to clear their lines, Coleman broke down the right flank only for Al Habsi to block his shot, with Pienaar eventually shooting over after a bit of penalty area pinball.
Moyes sent on strikers Jermaine Beckford and Victor Anichebe but their arrival allowed Wigan more space to break.
Beckford had the ball in the net, only to be ruled offside. Inthe final minute, Wigan sensed they could snatch a dramatic win when Phil Jagielka denied Mohamed Diame a chance and Howard made a fingertip save from Stam.
Moyes said: 'The crowd know we have been here before. Their anxiety iscoming from our form and the league position.'