City's 20-match unbeaten run came to an end as Branislav Ivanovic's first-half strike gave the Blues a vital victory, which moved Jose Mourinho's men level on points with the 2012 champions, who stay second in the table.
Leaders Arsenal are two points clear of the pair, but Sky Sports analyst Carragher reckons that City, whose next six league games are against Norwich City, Sunderland, Stoke City, Aston Villa, Hull City and Fulham, remain the team to beat.
Speaking on Monday Night Football, Carragher said: "It's a blow for City, but they are still right up there and you are going to get defeats through a season.
"The fact it was against a title rival may psychologically come into effect, but you see the next six fixtures and you'd expect City to win those games. I know the teams at the bottom are fighting for their lives, but the way they've been playing against those sides makes you expect they will win them all.
"They are still right in this title. Let's not forget Chelsea haven't gone above them. They have gone level with them and to do that they had to go to City. You'd still make City slight favourites, as the bookies do."
The best price currently available on City to win the title is evens, while Manuel Pellegrini's men are still odds-on with many high-street bookmakers.