Iván Ramis gave the Latics an eighth-minute lead when he struck a sensational first-time volley straight from Jean Beausejour’s corner.
Roberto Martínez’s men then made it 2-0 when James McArthur scored from the edge of the area, before James Tomkins netted a late consolation deep into stoppage time.
“It was a bit of a push on Winston Reid for their first goal but it was a brilliant volley,” Allardyce told BBC Sport.
“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.”
Meanwhile, Wigan manager Martínez heaped praise on his side for an excellent display which sealed their first home win of the season, reserving special praise for his Spanish defender Ramis.
“We don’t get too many goals from set plays but it was a tremendous finish from Ivan,” Martínez said. “That early goal set the tone of the game and allowed us to control it.
“I really enjoyed the performance. We have been showing flashes of our ability but today we were really good. Our philosophy and way of playing will never change.”
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