The Reds are now third, level on points with second placed Chelsea and just two points behind leaders Manchester City, with all three sides still unbeaten.
But Carragher, the former England and Liverpool defender, told Sky Sports that Mustafi should have prevented Mane from sending in the cross.
"You'd think Liverpool had lost the league after the game at the weekend because "oh it's two points dropped, Man City are gone two points clear", there's a long way to go".
Jurgen Klopp's men have done a far better job of keeping pace with the Manchester club this season and now trail the league leaders by two points.
Sterling was previously accused of lacking ruthlessness in front of goal, but he certainly seems to have addressed that issue, having scored 18 times in the league last season as he helped City to win the title.
As a result Firmino believes the Merseysiders are well placed to push City all the way as they seek a first league title since 1990.
"Last season it was like that, when we reached the Champions League final and also did very well in the Premier League, although City managed to open a good lead and did not give anyone a chance to catch up".
Jamie Carragher believes Raheem Sterling "deserves everything he gets" from Manchester City in relation to a new contract.
"It doesn't make sense to think like that because it puts you in a situation where you feel like you are not in charge".
"If they play on Friday and we play on Sunday, you think for two days from Friday until Sunday about the pressure being more on us because they have won already".
Firmino is confident he and his team-mates can lift a trophy come the end of the season, a belief which stems from the summer arrivals at Anfield.
The 31-year-old is down the pecking order at Juventus behind Giorgio Chiellini, Leonardo Bonucci and Andrea Barzagli and has made just four appearances this season in Serie A.
Could Liverpool pip Man City to the title?