Liverpool gave the ball away repeatedly in a shocking first-half display and were punished 10 minutes before the break when Hugo Rodallega struck from close range.
The Anfield club continued to make alarming mistakes in midfield and defence, while Fernando Torres missed the best of their chances when they did manage to threaten.
The result left Liverpool floundering with 48 points in sixth place - a point behind Tottenham Hotspur and Manchester City in the race for fourth and a shot at making the Champions League next season.
To compound the problem, Liverpool have played a game more than Spurs and two more than City.
Aston Villa, three points behind Liverpool but with three games in hand, are also looming. Wigan climb two places to 14th with 28 points after registering their first win over Liverpool in 12 attempts.
Liverpool manager Rafael Benitez hit out at his side's poor attitude.
"We have to show more character if we want to be in the top four," he told ESPN.
For a side brimming with talent Liverpool were well below par and had precious few clear-cut chances, Spain striker Torres spurning his side's best opportunity with 15 minutes remaining when, unmarked in the box, he rolled a shot hopelessly wide.
Liverpool now have just nine league games to rescue the situation, but even though their next league game is against bottom club Portsmouth at Anfield Benitez was in no mood to talk about a potential victory.
"We cannot guarantee anything without character or attitude," the stony-faced Spaniard said.
The only piece of positive news for Liverpool was the return of England defender Glen Johnson, missing since December after suffering a knee injury against Aston Villa.
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