The Reds boss fielded strong line-ups against Exeter and Brighton in previous rounds and will look to do the same against Stoke at the Britannia Stadium tomorrow.
Dalglish said: "We take it seriously and we'll be going to try and get a result. It's a trophy and we'd love to win a trophy at some stage.
"We've made several changes for both games and the way the players went about their work was a great reflection on the pride they have in themselves and also the football club.
"It will be the same for us at Stoke. They are a Premier League club and we'll put a very strong team out again. We expect the same level of commitment and effort from the players.
"We cannot guarantee anything other than we're going to work hard to try and get a result.
"We won't try and kid anybody that we're underestimating the tournament."
Dalglish is content with how Liverpool have been performing but wants his forwards to start converting more chances.
The Reds were held 1-1 at Anfield against Norwich on Saturday despite dominating large parts of the game.
And King Kenny added: "We don't want to get into the habit of saying we played really well and got nothing. We've got to make our good play count.
"I think overall in the game, most of the things we did I am very happy with. If we can create that many chances, or half that many chances, in a lot of games we'll score four or five.
"But it's all very well and good creating the chances, we've got to make the goalkeeper work a little bit harder as well.
"The most pleasing thing was the way the players cut Norwich open.
"I'm sure there will be a lot of games where we're a lot worse than that and come away with three points. The sooner that happens, the better!"