Bellamy returned to action little more than 48 hours after being withdrawn from the squad for Sunday's clash with Manchester City on compassionate grounds following the death of friend and former team-mate Gary Speed. And in the second half Bellamy came alive, setting up goals for Maxi Rodriguez and Martin Kelly as Chelsea were swept aside.
"Craig is a fantastic footballer who had a hugely disappointing day on Sunday. He regarded Gary Speed as a mentor," said Dalglish.
"It was great for the wee man, making the first goal. For the second he took the free-kick. He told Martin to leave it, it was going in!
"I don't know if we took Chelsea apart but we were delighted with the way we played. We've had a good day and we deserved to go through."
The scrutiny of Andre Villas-Boas' position as Chelsea manager will intensify after the exit from the Carling Cup, brought about by their third home defeat in four games.
Villas-Boas admitted Stamford Bridge had become anxious and called for fans to throw their support behind the team in the crucial forthcoming fixtures against Valencia and Manchester City.
"Away from home we've been more solid statistically and as a team. At home we just haven't been good enough," he said. "We need to get our fans behind us and get the emotions right. You can feel Stamford Bridge has become anxious. We therefore need support. We need atmosphere to get us past this period.
"We have two big games at home where we need our fans behind us and I'm sure they'll do exactly that.
"Our performance was not good today. Our best period was when it was already 2-0. Liverpool came very strong in the second half and caused us many problems. It's a pity because we had a good chance to progress at home, but Liverpool were superior."