Roberto Martínez’s side took a first-half lead when Martin Skrtel was penalised for fouling Wigan striker Victor Moses – and Shaun Maloney opened the scoring from the spot.
Steven Gerrard and Luis Suárez combined to level in the 46th minute, but Gary Caldwell netted the winner with 25 minutes remaining to condemn Liverpool to their fourth defeat in five league games.
“I think we looked a wee bit tired,” Dalglish said. “We had a lot of possession in the game but we gave away the ball quite a lot in vital positions. It’s not because they can’t play, it’s because of tiredness.
“If you play Sunday-Wednesday-Saturday it’s going to take its toll. A lot of the lads had played all three games, and for us that’s a reason behind our performance.
“It’s because of the demand on them with games, and we’ve not had enough players at our disposal to give them adequate rest.
“It’s a problem we face and it’s dictated to the clubs and the players by the television schedule. The fact we’ve done well in two cup competitions has obviously given us lots of extra fixtures.
“We’ll accept our progress in the cups and we’ll have to accept that we’re going to be a little bit tired. If we’re going to be successful we’ve got to be able to handle it.”
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