The Reds dropped crucial points in the Premier League title race last weekend following a 1-1 draw with Arsenal at the Emirates Stadium in the English capital.
James Milner broke the deadlock in the second half but Liverpool FC were denied three huge points when Alexandre Lacazette levelled with eight minutes to play.
The Merseyside outfit hoisted themselves to the top of the Premier League table before dropping to third place following victories for Manchester City and Chelsea FC on Sunday.
Liverpool FC entered the 12th round of fixtures in third place and two points adrift of the defending Premier League champions.
Manchester City have showed no signs of making a misstep in the title race following nine victories and two stalemates so far, dropping points in draws with Liverpool FC and Wolves.
Pep Guardiola’s side are looking to win the Champions League for the first time in their history, having reached the semi-finals on one previous occasion under Manuel Pellegrini.
Former Liverpool FC defender believes Manchester City getting distracted by the Champions League could be in the Merseyside outfit’s favour.
“I think Liverpool’s hope of winning the league is in the second half of the season if City go far in the Champions League, and hope that their focus is on that, taking their eye off the ball slightly,” Carragher told Sky Sports.
“That’s the only chance Liverpool have got, because City are better than them. But I think for the supporters and everyone around the club, Jurgen Klopp speaks very well and so do the players about the situation – Liverpool have made a brilliant start.”
Liverpool FC have significant ground to make up after the Reds ended up 25 points behind Manchester City in the Premier League table last term.
The Merseyside outfit signed AS Roma goalkeeper Alisson Becker, Stoke City playmaker Xherdan Shaqiri, AS Monaco star Fabinho and RB Leipzig playmaker Naby Keita in the summer.
Liverpool FC have lost to Napoli and Red Star Belgrade in the Champions League this season to leave last year’s runners up facing possible elimination at the group stage.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news