Scot is unhappy with the assessment offered by the former Red after the Cottagers’ 5-2 loss to the Anfield team and insists that there is always pressure on Merseyside
The 34-year-old spent seven years plying his trade on Merseyside, before moving on to Charlton Athletic, Tottenham and now Fulham.
The former Red had insisted that the resurgence after manager Roy Hodgson's exit did not mean that the club could mount a title challenge next season, pointing out after Liverpool's 5-2 victory over his side that the pressure to win may not have been as much as it is at the top.
According to The Guardian, Dalglish said: "He [Murphy] should know there is always pressure here. He played here long enough, didn't he? I just know that we played fantastic that night against Fulham and so does he.
"There's always a caveat in there somewhere, isn't there? There's always somebody that asks a question. But if you take any pride in your work, you are under pressure in any walk of life. It's not just exclusive to football. You worry about their ability to play first, and I'm sure the players can handle anything else that comes with it."
Now the Scot hopes that there is an improvement in the coming months and says everyone at the club can now look forward to next season.
"The expectation is for everybody to build on what has happened since January, have a good summer and go into every game with the same attitude and commitment as we have shown since January," said Dalglish. "If you put those things in place, then we aren't going to be too far away.
"Everyone is looking forward to next season, which wouldn't have been the case if we had stayed 12th. The fans are looking forward to it and so are the players. The disappointment of earlier in the season doesn't do them any harm, because once you win a couple of games you see how enjoyable it is. We only need to show improvement, and that will be a successful season. If we improve on what we've done this season next season, then I don't think anybody can be disappointed."