"We know he's a fantastic footballer and he had a hugely disappointing day on Sunday when Speedy, someone he regarded as a mentor, passed away," said Dalglish after the game.
"For someone to come back and play like that speaks volumes for him, but we're delighted with the way we played as a team.
"The way we are progressing is significant, especially in a cup that's been cheapened by the actions of the people who run it."
Dalglish also had something to say about the decision to play the game only 48 hours after Sunday's match with Manchester City.
"At least we've got a home game now, but we deserved to go through and we've got our reward," he added.