The Reds conceded the first goal after Martin Skrtel conceded a penalty which was converted by Shaun Maloney, and a second at 1-1 against the run of play after Gary Caldwell took advantage of a deflection to fire past Pepe Reina.
The manager told reporters: "We were disappointed because a lot of the final balls and good positions we didn’t deliver. I just thought we looked a bit tired.
"We had a lot of possession in the game, we gave away the ball a lot in vital positions and it’s not because they can’t play, it’s because of tiredness. We’ve not got enough players to give them adequate rest."
Dalglish’s side had a good spell after going behind in the first-half, equalising after 47 minutes as Steven Gerrard combined with Luis Suarez before setting up the Uruguayan for his goal, however for most of the match they struggled to break through Wigan’s defence at Anfield.
The club therefore remain in seventh place, a distant 13 points behind the top four Champions League places, and the Liverpool manager believes the club’s efforts in the FA Cup and League Cup competitions has taken its toll.
"It’s a problem given to the players by the television schedules and maybe the fact that we’ve done well in two cup competitions obviously has given us lots of extra fixtures," he added.
"If you play Sunday, Wednesday, Saturday it’s going to take its toll and a lot of the lads there have played three games. But it doesn’t matter how well you play, you’re still going to need a little bit of luck sometimes."
Suarez had a goal disallowed for handball shortly after his equaliser, and replays appeared to confirm that Uruguayan bundled in Skrtel's far post header with his hand.
When the manager was told of the decision he responded incredulously however, telling reporters: "It hits his left hand? I must have a different telly.
"We can’t control referees, we can only control ourselves. It just makes it more difficult when you don’t get the bounce of the ball."
He went on to reassure the club’s supporters that the side would benefit from the recovery time ahead of next weekend’s match against sixth-placed Newcastle, concluding: "We’ve got a week's rest before we play Newcastle next Sunday, so we’ll make the best of that."
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