On Wednesday, former manager Gérard Houllier said Dalglish had made a good start to his second reign at Anfield after guiding the Reds to Carling Cup in February.
However, the former Aston Villa boss believes the 61-year-old will fail to appease Liverpool supporters unless he can guide them to their first league crown since 1990.
“I don’t know how you define the word ‘obsession’,” said Dalglish. “It would be fantastic for Liverpool Football Club to win the league.
“We’ve won plenty in the past. It’s been a while since the last one, and it’s an ambition for everyone who supports Liverpool to see them win the league title.
“But, at the end of the day, there are a lot of other games to play other than league matches, and we want to compete in every game we play in.
“I’m not obsessed with anything other than the next game.”
Meanwhile, Dalglish conceded that his Liverpool squad is struggling to cope with injuries, with Charlie Adam and Daniel Agger unavailable for the trip to St James’ Park on Sunday.
“The strength of a squad is the way it handles suspensions and injuries and loss of form,” the Reds boss added.
“We’ve got a very strong squad that has been stretched, but there are a lot of other people in a similar position, whose squads have also been stretched.
“We were stretched at the weekend. A lot of them had three games in six days but the clear week we have gives everyone a chance to get rid of any bumps and bruises they have.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news