Norwich can look forward to another season of Premier League football after QPR were thrashed by Chelsea.
The 6-1 drubbing means Norwich are now safe from relegation to the Championship, softening the blow of their 3-0 loss to Liverpool at a rain-swept Carrow Road on Saturday.
Manager Paul Lambert says his side will bounce back after going down to a stunning hat-trick from Luis Suarez.
The Uruguayan struck twice in the space of four minutes midway through the first half to put the Reds in command.
After Norwich rallied briefly, Suarez completed his treble eight minutes from time with an audacious lob from just inside the hosts' half to give Dalglish's men the perfect tonic ahead of their FA Cup final date with Champions League finalists Chelsea next Saturday.
Reds captain Steven Gerrard had been restored to the starting XI after being rested for last weekend's disappointing home defeat by West Brom, which was a seventh in 10 Premier League games, as the visitors produced a composed display.
"It was a great performance, but that was not a surprise because we have produced that many times this season and not got our just rewards," said Dalglish.
"There are always going to be some great individual performances and Luis will get the headlines, and deservedly so, for three brilliant goals, but it was the way we went about the game which got us the result.
"We did not lose any goals, so there were some great defensive performances as well."
Suarez proved too hot to handle for the Norwich defence all afternoon, and kept his cool despite constant barracking from the home support.
"We are not surprised by Luis because of the quality of the player he is," said Dalglish, who revealed striker Andy Carroll had a slight groin injury which should clear up in time for the midweek Premier League game with Fulham and the cup final.
"It was a fantastic hat-trick, and (he is) a fantastic person.
"He has always been comfortable at Liverpool and we are delighted to have him.
"We are fortunate to have him playing for us, when he is playing like that it is very difficult for anyone to stop him."
It would've taken a Herculean effort from the sides below them to see Norwich dragged down into the bottom three.
Nevertheless, but for a rally at the start of the second half, Norwich rarely threatened the Liverpool goal.
Indeed the Canaries - who were thrashed here 6-1 by Manchester City a fortnight ago - were architects of their own downfall for the opening two goals, paying for some sloppy defending.
Norwich manager Paul Lambert, though, prefers to look at the bigger picture, having overseen successive promotions up from npower League One.