The Reds have enjoyed a solid start to the Premier League season but still have ground to make up on the top four and will hope to stay in contention by beating Aston Villa on Sunday.
Dalglish does not believe Liverpool are far away from challenging the elite group once again and has called on his men to keep working hard.
"We've been delighted with what we have done," said the manager.
"We'd love to progress into the top four and the best way to do that is to do what we do well.
"It is only slight but, then again, some of the smallest steps are the biggest ones to take."
Manchester City and Manchester United currently lead the way in the title race and Dalglish insists they are both extremely strong teams despite being knocked out of the Champions League at the group stage.
The London trio of Chelsea, Tottenham and Arsenal are also ahead of Liverpool going into the festive period but Dalglish is ready for the challenge.
He added: "Of course it's going to be tough. The teams that are there or thereabouts are really good sides.
"Two of them got put out of the Champions League but there are still really good sides here.
"It's going to be tough but we'll have a good go and see where it takes us.
"We'll look to get the points by playing as well as we have done and getting that wee bit of extra luck.
"We believe we are doing things the right way so we'll continue to do that because we don't know any other."