Steven Gerrard's early penalty gave the Reds a first-leg advantage in the Carling Cup semi-final clash at Etihad Stadium on Wednesday.
After the match, Dalglish reflected upon a game of two-halves while crediting his side for their determination and grit to hold on to the win.
"There were two different performances in each half; first half we looked a little more threatening but in the second half, having got the goal advantage, we battened down the hatches and tried to get through it with no goals against us," said the Scot.
"Not too many teams have come here and gone away with no goals against them.
"It was a fantastic effort by the players in the second half - it might not have been the prettiest performance but it did not fall short of desire.
"Once we got ourselves in front we were determined not to lose it.
"They are always a very difficult team to break down, they are a fantastic side and that is why they are top of the league.
"To be fair Pepe (Reina) had a good save from Richards' header and from (Samir) Nasri in the first half.
"If you come here and win 1-0 you are not going to be unhappy. It is a fantastic performance by the players against a team that are a really good side."
Despite coming out on top in the first-leg, Dalglish was taking nothing for granted in the return leg in a fortnight's time.
"We might have the slight advantage with the goal but it does not mean to say there will be anyone jumping through hoops at our place - we will just go and be professional in the second leg," he added.
"We have to be happy but we are not presuming that the job is done."