With nine matches remaining, the Reds are a point adrift of Tottenham, but Spurs, Manchester City and Aston Villa all have games in hand as they battle it out for fourth place.
Liverpool travels to Lille in the Europa League on Friday but could trail Spurs by four points by the time it returns to Premier League action against Portsmouth at Anfield next week.
Benitez was bitterly disappointed by the manner of the loss at the DW Stadium, Liverpool's ninth in the Premier League this season.
He was at a loss to explain why Liverpool had put in such a poor performance at a crucial stage in the campaign.
And the Spaniard said a repeat of that display would end its chances of reaching the Champions League.
"We didn't show attitude and we were behind, and after that we were working very hard but working hard without game intelligence," Benitez said.
"When you approach the game like we did tonight you cannot win these kind of games, or maybe any game."
After Fernando Torres hit the post for Liverpool, Hugo Rodallega scored the only goal of the game, making the most of Dirk Kuyt giving the ball away on the edge of the area.
It was Wigan's first win in eight Premier League matches and its first victory over the Anfield club.
With a trip to fellow struggler Bolton to come on Sunday, Wigan, which was playing on a relaid pitch for the first time, moved four points clear of the relegation zone.
Manager Roberto Martinez feels his policy of playing attractive football has been vindicated.
"It was a huge win because it has been coming," Martinez said.
"It's huge for confidence but we're far away from our aim of staying in the Premier League and giving us the chance to carry on improving and growing."
