Craig Bellamy marked his second full debut for the Reds by finishing neatly from a tight angle in the seventh minute on the south coast.
Brighton upped the ante in the second period but Dirk Kuyt doubled Liverpool's advantage, before Ashley Barnes pulled one back from the penalty spot.
As well as bringing a win, the match also marked talisman Steven Gerrard's return to action after six months out with a groin injury.
"I thought the first-half performance was fantastic from the players," Dalglish said.
"The performance was especially pleasing for the way they responded to the disappointment we shared on Sunday [in the 4-0 defeat at Tottenham].
"They were a great credit to themselves and the football club by the way they went about their work.
"Some of the football with the passing and movement in the first half was exceptional.
"Obviously it is very difficult to keep that going for 90 minutes.
"In the second half, Brighton got a little bit more into it but we always looked like we would get something on the break and that is how it proved to be.
"But it was a difficult game, a positive result and also very positive news that Steven got 20 minutes.
"But also [it was positive] for Jack Robinson to get a full game, Sebastian Coates getting a full game, Maxi (Rodriguez) got a game and played very well.
"Craig Bellamy scored on his return to the club so there were a lot of positives there and Martin Kelly almost got a full game so it was a good night for us."
The stand-out player of the evening was Bellamy, who shone from the outset and looked dangerous throughout.
The Wales international rejoined the Reds from Manchester City in the summer and Dalglish was quick to praise the 32-year-old.
"I thought he was fantastic," he said.
"When he came in we said he would make a contribution and it has not taken him long.
"He just loves playing football. He is really enthusiastic and fit.
"He loves the football club, he is a supporter of the football club.
"He wants to do it and do the best he possibly can for the club and we look forward to that."
Bellamy looked particularly dangerous in a first half that Liverpool dominated completely.
Brighton only managed to eke out one attack in the opening 45 minutes but were much improved in the second half.
The defeat was the Seagulls' first at the Amex Stadium but manager Gus Poyet was buoyed by his side's response after a poor first-half showing.
"It was an easy half-time meeting," he said.
"There are some days when you are sitting there and thinking 'what am I going to say?' but today was very easy.
"There were too many players desperate to play today.
"They were waiting for the game and we lost half an hour not being alert, not being aware of what is going on.
"Of course you need to pay credit to Liverpool because I think today the four more offensive players especially were outstanding.
"Maxi, Kuyt, Bellamy and [Luis] Suarez moved it around at their best. Passing the ball around, interchanging positions.
"It doesn't matter how good you are, it doesn't matter the system you play - if you play that quality you are going to suffer.
"But, saying that, we were not there as a team for some reason [in the first half] and that was the aim of the game today.
"Of course go and try to win it, but [we wanted] to see if we could be ourselves against anyone and we did it in the second half."