The Reds conquered the Canaries 3-0 after their Uruguayan striker scored twice in four first-half minutes for the visitors.
A sublime third goal from near the halfway-line from Suarez wrapped up the game with eight minutes on the clock for Dalglish’s men but he highlighted the solid performance from the whole team at Carrow Road.
“It was a fantastic team performance,” he told reporters after the match.
“Luis will deservedly get most of the headlines for three brilliant goals but the way we went about the game and approached the game got us the result.
“We're really pleased with the way they've committed themselves to the game today, as we were last week when we never got the result that the performance deserved.
“Every single one of the players in the squad could play for us against anybody.”
Norwich were far from outplayed but their defensive lapses cost them dearly as Liverpool finally showed the goalscoring potential they have sourly missed at times this season.
“They're a credit to themselves and they have been many times,” Dalglish beamed.
“The pleasing thing is that the performance was rewarded with the proper result.
After only bagging one win in their last 11 Premier League games, The Scot admitted he was cheered by his side's return to form that sees them hold on to eighth place in the league.
He admitted: “There was a smile on my face a few times. It was a great win and a great performance.
“The level of performance wasn't a surprise; they've produced that many times this year without getting this reward for it."
Suarez’s hat-trick was world class. His first a powerfully-hit shot on his left foot, the second from an acute angle on his right and a third, from 55 yards, was simply sublime and left Canaries keeper John Ruddy helplessly backtracking to no avail.
“He's a fantastic footballer and a fantastic person,” Dalglish said of his star striker.
“We're very fortunate to have him. When he plays like that, it's very difficult for anyone to stop him. It took him five minutes to settle on when he scored on his debut against Stoke.
“He's always been very comfortable at Liverpool and we're just delighted to have him.”
Dalglish refused to single out his favourite, despite the world-class quality in the third strike in the final 10 minutes.
“Every goal was a great goal,” Dalglish insisted. “It's no surprise because of the quality of the player.
“There were some great performances defensively as well; Pepe [Reina] has only had one save to make. [Jamie] Carragher was fantastic at the back.”
Andy Carroll’s omission from the squad raised a few eyebrows but Dalglish is certain he will be fit for the FA Cup final against Chelsea next Saturday.
“Carroll just has a niggle in his groin,” he said. “He will be fit for the Cup final.”