The Reds have made an indifferent start to the 2017-18 campaign, winning just three of their opening eight games in the top flight, succumbing to Leicester City in the Carabao Cup and recording just a single victory in their opening three European group games.
The run follows a summer transfer window in which Liverpool signed just four new players in the form of Mohamed Salah, Dominic Solanke, Andrew Robertson and Alex Oxlade-Chamberlain.
Rivals Manchester City, Manchester United and Chelsea made swathes of additions, with the trio occupying three of the top five positions in the table and on course to qualify for the Champions League last 16.
And Mills, formerly of Leeds United and City, believes central to the Merseysiders' problems is a lack of players of the calibre required to challenge for major honours.
"Their recruitment hasn't been brilliant," Mills told BBC Radio 5 Live after Liverpool's 7-0 win over Maribor. "They still need a number one goalkeeper, a dominant centre-halve or two, a really strong powerful midfield player and a centre-forward who can score 20 plus goals a season. They are still three or four players missing to win the Premier League. They are five or six players to win the Champions League.
"They could have sold Coutinho for £130m. If money is the issue why they can't bring in other players, then sell Coutinho. You've got Lallana, you've got other players. You've just brought Oxlade-Chamberlain, even Firmino can play in those sorts of areas. They've got cover and a lot of similar players.
"Look at what all the other big teams have done. United have brought Zlatan [Ibrahimovic] in now. If you go back in time United brought in Robin van Persie aged 30-something. Sometimes you need a player who is going to play for this season, next season and that is it. Just write it off. You can't keep building for the future because the future will never come."
Following last weekend's dire goalless draw with United, Klopp's men face another test of their lofty ambitions when they travel to Tottenham. The German coach has an impressive record against other sides in the top six with nine wins from 21 games with just two defeats.
While Liverpool were sweeping aside Maribor, Tottenham gained a credible draw with Real Madrid at the Bernabeu to stay on course for the knock-out stage.