The Reds claimed a 1-0 win at the Etihad Stadium, giving them the advantage heading into the second leg of the Carling Cup semi-final at Anfield in a fortnight.
"If you come here and win 1-0, you're not going to be unhappy are you?" said Dalglish. "It was a fantastic performance from the players against a team that are a really good side. We've got to be happy, but we're not presuming in any way, shape or form that the job is done.
"We might have a slight advantage with the goal, but that doesn't mean to say there is anybody jumping through hoops. We'll just be as professional as we can in the second leg."
The winners of the tie will face either Crystal Palace or Cardiff City in the domestic cup final.