Bellamy scored in the 2-1 Carling Cup win against Brighton on Wednesday after being given his first start since re-signing for the Anfield club last month.
Despite the 32-year-old's reputation for having trouble follow him wherever he goes, Dalglish has had nothing but praise for a player they picked up for nothing after Manchester City agreed to cancel the final year of his contract.
Bellamy left Anfield in 2007 after just one season but Dalglish believes he has returned with a determination to do better than his first brief spell, in which he scored nine goals.
"We knew what we were getting when Craig came in. We've said many times before what Craig brings to this football club," said the Scot.
"He had a year out last year when he played at Cardiff rather than in the Barclays Premier League and I think we are getting the benefit of that because he has got a hunger to come in and impress.
"He's got a desire because maybe he went away with a bit of unfinished business the last time he left here.
"So he's got a desire to relight that and we'll get the benefit of it.
"He'll make a contribution to the football club over the length of his contract and hopefully Wednesday night was just the beginning for him.
"He loves playing football and is really enthusiastic. He wants to do well and we'll help him to do that all that we can."
Meanwhile, Bellamy is looking forward to getting the chance to play alongside the "impressive" Luis Suarez more often.
"I managed to link up with Luis Suarez who is such an impressive player and it was a good feeling," he said about playing alongside the Uruguayan at Brighton.
"It was a nice goal and I was pleased with it."