Suarez ensured Liverpool supporters, dejected by the loss of Fernando Torres to Chelsea on Monday, had a new hero after coming off the substitutes' bench to score in the 2-0 victory over Stoke at Anfield here on Wednesday.
The £22.6 million signing from Dutch side Ajax gave Reds fans disheartened by a season of under-achievement reason to be hopeful after rounding keeper Asmir Begovic and although Andy Wilkinson got a boot to the striker's shot, he could only help it into the net off the post.
Suarez is now in line to start Liverpool's game with Chelsea on Sunday after an eye-catching 27 minute display.
And Dalglish, arguably Liverpool's greatest striker, believes Suarez will get even better as he adapts to the demands of the Premier League.
"He has not even had the opportunity to train with us," said Dalglish.
"There was administration stuff that needed to be sorted out. He got his work permit on Tuesday and was in the squad Wednesday. He has a big smile on his face every day. It is great to score on your debut and he worked hard."
Liverpool head for a reunion with Torres with their confidence sky high. They remain seventh in the Premier League but are just two points behind sixth-placed Sunderland after a third successive league win and a third straight clean sheet.
However, Dalglish refused to get carried away, particularly as Chelsea will kick-off with a nine-point advantage over Liverpool at Stamford Bridge.
"It's an old adage and I'm sure you'll cringe, but we will just take each game that comes along," the former Scotland forward insisted.
"That is all we will do and then at the end of the season we will add our points up and see what we have got.
"We will not get carried away -- there is a lot of hard work ahead. Three clean sheets is always a bonus and always a help.
"It has been a busy week. We have been in the papers more than we have wanted to be, but great credit to the players, they have just gone on with it. We have a group of players who want to compete for everything."
Andy Carroll, who Liverpool signed from Newcastle for £35 million on Monday as a replacement for Torres, witnessed the Stoke victory, but the striker is still several weeks away from making his debut because of a damaged thigh.
But Dalglish believes an in-form Suarez and a fully fit Carroll is an exciting prospect for Liverpool fans.
"Andy is going to be a few weeks before he is fit," he added. "But we bought him for five years so being out for a few weeks wont do us any harm."
Even Stoke manager Tony Pulis was full of praise for Suarez.
"I don't think you need me. . . .it's all about their new lad isn't it?" he said after his side's third defeat in four league games.
"We're quite happy for the lad to claim it (the second goal). If I was Kenny, if he was half a yard near it then it's his goal."
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