Ian Rush has hailed Liverpool's ability to grind out results but is now calling for them to start winning in style.
The Reds legend is delighted Rafael Benitez's side have taken maximum points from their opening two league matches and now wants them to step it up a gear in terms of performance levels on the pitch.
"You can't ask for any more from a team than to take six points from their first two games of the season and that is exactly what Liverpool have done," said Rush.
"Sunderland and Middlesbrough are going to give a lot of teams problems this season but, despite being nowhere near their best, Liverpool have somehow managed to come up with a way to beat both of them.
"In this respect, you can't ask any more of Rafa Benitez and his players. They have done just what we all hoped they would do in terms of getting off to a good start.
"But there is no doubt they are going to have to improve if their winning run is going to continue because their opening two performances have not been of the standard expected."
Rush admits developing a habit of 'winning ugly' is essential if the Reds are to challenge for the title but believes it would be unwise to suggest they don't need to raise their game in the weeks ahead.
"Winning when you are not playing well is something you have to be able to do if you are going to challenge for the title but it isn't something that can be sustained too long," he said.
"If you're sloppy in possession and not creating many chances then it is inevitably winning matches is difficult.
"That's what happened against Middlesbrough on Saturday when Liverpool didn't get anywhere near hitting the kind of form they are capable of. They could so easily have dropped valuable points.
"The fact that they didn't though says a lot about the character of the team and I'm sure that's one of the big plus points that Benitez is taking from the game."
Liverpool needed two goals in the last five minutes to see off Middlesbrough on Saturday and Rush wasn't surprised that it was the club's home-grown duo who stepped up to the plate.
"When things aren't going well you need your big game players to pull something out of the bag and that's what Jamie Carragher and Steven Gerrard did.
"When things aren't going well it can sometimes be easy to just accept that it isn't going to be your day but that's never going to be the case with players like Carragher and Gerrard.
"In taking the initiative they led by example and it was thanks to their interventions towards the end of the game that Liverpool were able to come away with three points they might otherwise have missed out on.
"The concern is that Liverpool cannot continue to rely so heavily on their captain and vice captain and other players are going to have to start chipping in if the good start to the season is to be maintained.
"I know the fans will be concerned about Liverpool's current form but the most important thing at this stage is to get points on the board.
"If you do that then it breeds confidence and it sends out a message to the rest of the league that you are going to be hard to beat.
"But Liverpool need to get better and I believe that they will, especially if Benitez can add a bit of width to his side before the transfer window closes."
One of the major positives that came out of the 2-1 win over 'Boro' was the partnership of Robbie Keane and Fernando Torres.
The duo have begun to show signs that they could well develop an understanding to rival any in England and Rush is confident they will make it work in time.
"There were welcome signs against Middlesbrough that Fernando Torres is beginning to strike up an understanding with new strike partner Robbie Keane," he said.
"You could see that they were starting to get used to each other's movement and were picking up their running off the ball.
"There was one moment in the first half when Keane went on a little run and picked Torres out with a perfect pass with the outside of his right foot.
"Torres wasn't able to take the chance on this occasion but at least it showed that they are getting to know one another better and that bodes well for the future.
"If these two hit it off, and I've got no reason to doubt that they will, then it will really benefit the team as a whole and I'm sure they're both working really hard to make it happen."
Rafael Benitez and his side now head into tomorrow night's Champions League qualifier with Standard Liege determined to improve on their showing in the first-leg in Belgium.
Rush feels the Reds cannot take progress for granted and expects the Belgian champions to give them a tough test.
"Anyone who saw the first leg of Liverpool's Champions League qualifier against Standard Liege a fortnight ago will know the Belgians are no pushovers," he said.
"Standard are the champions of their country and that means they deserve respect, especially after the way they performed against the Reds in Liege.
"Had it not been for Pepe Reina's heroics then Standard would be coming to Anfield tomorrow night with a lead to protect and that would definitely have made the tie even more difficult than it already is for Rafa Benitez's men.
"As things stand, Liverpool do not have an away goal to fall back on so they will be looking to keep a clean sheet otherwise things could get very tricky.
"Obviously, Liverpool are big favourites to go through but they cannot take anything for granted because if they do Standard might just take advantage.
"Importantly though, Liverpool have encountered this kind of situation so many times in Europe in recent seasons so they know exactly what they have to do and how to go about it.
"I wouldn't be at all surprised if it is a tight affair because Standard looked a well organised and decent side in the first leg but Liverpool should have enough know how and experience to get through."