Off-field matters had dominated pre-match proceedings as both sides tried to ease tensions ahead of the first meeting of the two sides since Luis Suarez's eight-match ban for racially abusing Patrice Evra.
However, there were very few flashpoints in a game which lacked a little of the ferocity usually seen in such encounters.
Dirk Kuyt's 88th-minute goal proved decisive, after Daniel Agger's header had been cancelled out by Park Ji-sung before half-time, as Liverpool made it two cup victories three days having reached the Carling Cup final in midweek at the expense of Manchester City.
"It was a fantastic effort from our players after what they had to get through on Wednesday night," said Dalglish.
"To ask them to come back and play again on Saturday morning was pushing it a bit too far.
"Their commitment, attitude and desire to get a result was fantastic and we cannot speak highly enough of them after that performance and result today."
Evra was booed throughout by Liverpool fans but other than a few expletive-filled chants and a couple of antagonistic banners nothing untoward happened inside the ground.
"I think both sets of fans were a magnificent advert for their clubs," added Dalglish.
"Both clubs can be very proud of the fans they have here. There was a good bit banter between both fans, which is brilliant because you don't want to take that away.
"I think in the main they were fantastic and the players were a credit to that because none of them tried to do anything other than play football.
"They (United fans) will be disappointed at losing but they deserve credit for contributing to the occasion.
"That is what the players did and the fans did; the fans are entitled to support their team, absolutely no problem.
"I don't think there was anything there that was untowards."
Dalglish also praised Kuyt and Andy Carroll, who played a part in both goals by occupying goalkeeper David de Gea for the first and flicking on Jose Reina's kick for the winner.
"He is good in the air but he we have to develop that, he has to develop it and he has got to work within our framework as well," he said of £35million record signing Carroll.
"We will work with him and we will be a lot more patient than a lot of people.
"I am sure we will get the rewards in the end but they are starting to bear fruit now."
On Kuyt he added: "It is a fantastic day for him and the club to go through to the fifth round after beating Manchester United."