Goals from Ivan Ramis and James McArthur secured the three points but Allardyce was much more disappointed with his own side's performance.
The Hammers manager told BBC Sport: "It was a bit of a push on Winston Reid for their first goal but it was a brilliant volley.
"And they deserved to win. We didn't play any football today, we didn't get past half-decent. We weren't good enough to get anything and I'm disappointed our performance has reduced to such a level.
"It wasn't about Wigan today, it was about us not using the ability we've got. We can't keep giving the ball back to them."
West Ham have slipped to ninth in the table following the defeat.