A promising campaign has so far been undermined by the fact that both luck and quality have too often deserted the Reds in front of goal.
They have struck the woodwork 18 times, more than anyone else in the Premier League, while their tally of 24 goals is the worst in the top six.
"As I've said many times before, I don't think the players have had their reward for the performances they deserve,” the Scot told the club's official website.
"Maybe January 3 [against Manchester City] is going to be the game we get the little bit we deserve for the great play, effort and commitment the players have put in. We'll keep our fingers crossed.
"To get 2011 out of the way was good for us because I don't think we've had too much luck in the matches we've played in the first part of the season."
Dalglish is very aware of the challenge posed by Roberto Mancini’s expensively assembled squad of stars, but remains confident his side can compete, just as they did in a 1-1 draw at Anfield back in November.
"We'll have a look, see how we're going and how we're going to play,” he added.
"We've got the utmost respect for what they've done. It's all very well and good saying they've got a lot of money, but they've also got a good team.
"We'll just go and play whatever 11 they put on the pitch. It doesn't matter what they cost. We'll give a lot for the football club and try and get a result."
Liverpool have been boosted by the return of captain Steven Gerrard from a lengthy injury layoff but while Dalglish admits he is happy to have his talisman back, he appears wary of putting pressure on him by placing too much significance on his recovery.
"We're delighted to get any one of our players back,” the Scot insisted. “Everyone of our players we value.
"They're all very important to us and we'll respect and appreciate everything they do for the football club.
"Some will get more credit than others, some might get a bit more stick than others, but they all put in a good shift and we're delighted with the efforts of every player that's been here, especially in the first part of this season."
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