Papiss Cisse's brace left the Magpies level on points with Chelsea in sixth place in the Premier League, two points behind fourth-placed Tottenham ahead of the latter's clash with Swansea and five behind Arsenal in third.
Liverpool are eighth, behind Everton after a sixth defeat in seven Premier League games, but Dalglish is convinced they should have had a penalty when Danny Simpson handled on the goal line with the score still goalless.
However, he had no complaints about Reina being sent off for headbutting Magpies defender James Perch.
"We had chances and we were unfortunate not to get a penalty, and that would have left us playing against 10 men," Dalglish told Sky Sports News.
"Then they got the goal, which from our point of view was disappointing, and the boys showed frustration and maybe started feeling sorry for themselves.
"Pepe got frustrated and got himself a red card and Andy marched up the tunnel (after being substituted), he was frustrated and disappointed for himself and at the result.
"There's no problem with the red card for Pepe but there is a problem that we never had a penalty kick."
On Carroll's booking, he added: "I don't think it was a penalty but neither did I think Andy was trying to get a penalty.
"The decision not to give a penalty was correct but it was harsh to show him a yellow card, he was always struggling to keep his balance."
Opposite number Alan Pardew had a contrasting view on the Simpson incident and also defended the decision to award his side's second goal, when Cisse was clearly offside when Demba Ba passed the ball but onside from the resulting touch on by Hatem Ben Arfa.
"That little touch, by that time the Liverpool player is level and he's onside," Pardew said. "It's a rule none of us managers like but that's how it is."
On the penalty appeal, he added: "It hit (Simpson) high on the shoulder, I'd be very surprised if the referee gives that - it's not a hand sticking out, I thought it was fine.
Mike Williamson, meanwhile, was delighted by the win which kept the Magpies' top-four hopes alive.
"It's massive, it keeps the momentum going and the dream alive of as high a finish as possible," he said.
"If we keep playing like that and working hard then anything's possible."
Goalkeeper Tim Krul paid tribute to Williamson and his stop-gap fellow centre-half James Perch, who admirably filled the void left by Fabricio Coloccini's absence.
He told Sky Sports 1: "(Williamson) and Perchy were outstanding, they blocked everything - I didn't have to make a proper save today."
And the Dutchman also saluted the prolific Cisse, adding: "He's a fantastic striker, a proper goalscorer. He's a typical number nine for Newcastle and I'm happy we signed a top-class player like him."
His predecessor in that illustrious shirt, Andy Carroll, endured another forgettable day for Liverpool, which included a booking for simulation after tumbling over when Krul challenged him in the penalty area.
"He just went over, he dived, I never touched him," Krul said.
"He was looking for a penalty, all strikers try to do that, but he didn't get it, the ref was at a good angle to see it."
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