The loss means that Dalglish's side now trail sixth-placed Newcastle by 11 points with seven games of the season remaining, but it was their indiscipline that brought a stinging rebuke.
Andy Carroll and Pepe Reina both came in for criticism from their manager after moments where both men lost their head. Carroll, who was cautioned for a dive in the first half, launched a furious and abusive tirade towards his own dug-out when he was substituted in the 80th minute.
The former Newcastle forward, who endured a painful first return to St James' Park since he was sold to Liverpool for £35 million 13 months ago, reacted to the decision by appearing to mouth, "Effing joke this", before swearing at his own bench.
He then stormed down the tunnel without acknowledging either Dalglish or any of the Liverpool backroom staff. Three minutes later Pepe Reina was shown a straight red card when he aimed a headbutt at James Perch after the Newcastle defender had gone in late for a challenge. The dismissal bans the Liverpool goalkeeper for three games, ruling him out of the FA Cup semi-final with Everton later this month.
"We have not got a problem with people showing desperation or disappointment or frustration but we need to channel it better than we have done," said Dalglish.
"It ended up with a lot of frustration and disappointment and I think the frustration and disappointment was a result of the actions that Pepe took. He got a deserved red card, and then Andy came off and went up the tunnel. He was frustrated with the way the game had gone. Not just for himself but for the team.
"We have got to believe in ourselves. If we do that, then we will have a better opportunity. We have no qualms either about when Andy went down with the goalkeeper. I thought it was not a penalty kick. I also thought Andy was losing his balance anyway.
"Even if he had got past the goalie, I think he would still have fallen over. We don't have a problem with that. We might have a problem with the yellow card because I don't think it was intentional, him looking for a penalty kick.
"Some of the football we played in the first half was good and exciting. Maybe with a bit of luck and composure we could have been in front. The goal we lost, the first one, we can learn off. But we will stick together. The best way out of it is to stick together.
"They believe in what they are doing. It is not as if they don't have the determination and the effort. If they start to enjoy losing games, then we will have a problem."
Dalglish revealed that Reina had apologised to his team-mates for his red card. "There was a bit of remorse there, yes," he said.
Liverpool were denied a penalty when Danny Simpson handled on the line, but this was another day when Alan Pardew's side showed why they have been one of this season's surprise packages. Two goals from Papiss Cisse, who was allowed to eat curried goat on Friday at Newcastle's training ground as part of an African Day, secured their win.
"It was his best performance yet for us," said Pardew: "We have the new No 9 but I felt for Andy today. He is a terrific lad and has had a tough year, but from our side of the coin we have Cisse and long may his form continue.
"If someone said we would be in the Europa League after this season I'd snap their hands off. Hopefully we will get enough points to get into Europe. We have an assurance about us at the moment, and a discipline."
Red and buried
Liverpool have lost six of their last seven league fixtures:
11 February: Manchester United 2-1 Liverpool
3 March Liverpool 1-2 Arsenal
10 March Sunderland 1-0 Liverpool
13 March Liverpool 3-0 Everton
21 March Queen's Park Rangers 3-2 Liverpool
24 March Liverpool 1-2 Wigan Athletic
Yesterday Newcastle United 2-0 Liverpool
The games Pepe Reina is set to miss: Saturday: Aston Villa (h); 10 Apr Blackburn (a); 14 Apr Everton (FA Cup semi)
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