The Reds ran out 4-1 winners against Chelsea at Anfield on Tuesday evening, with the Scotsman also noting the role of goalscorers Shelvey and Henderson in the victory
Dalglish's side responded to Saturday's FA Cup final defeat to the Blues with an emphatic victory in Tuesday's Premier League clash, with the Scot appearing emotional as he saluted the Kop in a lap of honour after full-time.
“The way the fans stayed behind at the end, I'm not sure there's any other set of fans that would have stood there and shown an appreciation like that,” said Dalglish to reporters after the game.
“The result was thoroughly deserved and the supporters can go home for the last time this season with smiles on their faces.
“It was an excellent performance. It's been seen a few times here this season but the result hasn't been as pleasing as that.”
The result leaves Liverpool with a chance of overhauling seventh-placed rivals Everton on the final day of the season and Dalglish singled out a number performances from his players, including that of man-of-the-match Carroll.
He added: “The two boys in midfield [Jordan Henderson and Jonjo Shelvey] were great, big Andy [Carroll] was unplayable and Luis [Suarez] was fantastic.
“The old boy at the back [Jamie Carragher] didn't do too badly either but everybody played their part.”