The visitors headed for home licking their wounds from a worst defeat since August 2009.
Having established a winning position in less than an hour when Andy Carroll put them two goals clear, few would have forgiven the Reds for easing off considering they have a Carling Cup final showdown with Cardiff ahead of them on Sunday.
Instead, they kept powering on to book a quarter-final encounter with Stoke, registering three more goals and also failing with a Luis Suarez penalty.
And, though the bizarre fact of Brighton contributing half the Merseysiders' tally in own goals was an obvious talking point, Dalglish declared himself satisfied with the overall outcome.
"That is the proper way to show respect to a football team," he said.
"Although no-one wants to lose by six we haven't gone out there to undermine them or belittle them. We wanted to play well.
"Even when we went four, five and six up, my players were still trying to get another goal. They never turned off at any time.
"We would much rather have scored than the opposition but they all count and it wasn't as if we didn't create any chances.
"A lot of people who love this football club want to be entertained. That is what they got."
Dalglish believes in the team ethic too much to over-enthuse about any individuals.
And, the standard of opposition must also be taken into account.
However, on their first start together, there was no denying the effectiveness of Steven Gerrard, Andy Carroll and Suarez as an attacking unit.
Carroll has been pilloried since his £35million move from Newcastle in January 2011, the hefty transfer fee weighing him down.
It quickly became apparent on Sunday though that the only way Brighton could subdue the burly forward was through illegal means, with Adam El-Abd exceptionally fortunate not to concede a spot-kick long before Suarez fluffed his lines.
That was just about the only thing the Uruguay got wrong. After the events of recent weeks, Suarez will have to get used to the boos that cascaded from the visitors' end every time he touched the ball.
But, unselfishly set up by Carroll near the end, he now has two goals in as many games and his incisive running would appear the perfect complement to his strike partner's more direct approach, providing Gerrard can remain fit to supply the service.
"Those two did particularly well," said Dalglish, referring to Carroll and Suarez. "But I was pleased with everyone.
"It is important everyone did well. It is also important that we stick together as a squad and we don't get carried away with anything that we have done."
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