Lawrenson wrote in his column in The Mirror: "What a brilliant win for Liverpool. Say what you like about the standard of play, Anfield will be buzzing this morning and the confidence among the players will be sky high.
"When you consider the summer they have had, to start the season in the way they have done is a fantastic achievement. Sadly, I still don't see them in the top four at the end of the season.
"They are much closer to their target but I don't want to get carried away and say they will get there because I don't believe they will. There are just too many other stronger teams."
Liverpool are currently top of the Premier League and are the only team in the top flight with a 100% record.