The frontman was deployed in a lone striking role and after Steven Gerrard's 13th minute penalty gave Liverpool the lead, he became more and more isolated as the Reds were pushed back by Roberto Mancini's side.
But Dalglish was delighted with the committment shown by the goal-shy striker in the face of a tough evening up against City's powerful backline.
"Andy worked fantastically hard for us and sacrificed himself for the sake of the team," Dalglish told reporters.
"If our players continue to work as hard as he did last night - every one of them - then if we want to move in the right direction that will be a great start for us.
"And in the second half they sacrificed their own beliefs for the benefit of the team and they defended really well.
"There is nothing wrong with the commitment of this squad and if it were going to be put to the test it was going to be at City and they stood up to the test.
"There weren't many too many near misses for City and every single one stood up and was counted and sacrificed themselves for the team and I think everyone will have appreciated it."
Dalglish was also delighted with Steven Gerrard, who played the full 90 minutes as he ramps up his comeback from injury."For Steven to step forward and score with a penalty is great for us," the Scot continued.
"He is going to get better every time he finishes a match.
"He is certainly gaining the benefit. It is great to see him back and he has a great influence for us."