Manuel Pellegrini's side went into the game on a 20-match unbeaten run and with a perfect Premier League home record, but Branislav Ivanovic's solitary goal ensured those records were emphatically broken and denied them the chance to go back to the top of the table.
City were odds-on for the title with the bookmakers ahead of the Monday Night Football clash and whilst their odds have lengthened, they remain the shortest price to win the Premier League.
And Sky Sports expert Carragher says that forthcoming fixtures against Norwich, Sunderland, Stoke, Aston Villa, Hull and Fulham should see them make a real impact at the top of the table.
He said: "Throughout the season you look back at games that win you titles and those are the types of games. The reaction of Jose Mourinho and the players at the end showed you how important it is.
"That's six points they've taken off City and who knows how important that will be at the end of the season? Normally title winners beat their title rivals and they have done it twice now.
"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."
Chelsea are now level on points with Manchester City, two points behind leaders Arsenal, but Jose Mourinho played down their title chances after the game suggesting they were not yet ready to win the league this season.
Carragher was surprised by his modesty, but feels his failure to sign a top-class striker may be the reason why they won't win the Premier League this season.
"I think he knows the squad and I think he looks at the centre-forward situation. I think that's the only thing holding him back," he said.
"We always say it's difficult to get strikers in January, but I look at Liverpool and they got Suarez and Sturridge over the last few years in the January window.
"If he could have got one I think he would have got one, but the top strikers are all at top clubs, so where do you get them from? You look at Falcao maybe at Monaco, but he's got a bad injury now.
"As soon as he gets that centre-forward I think he'll be calling it on. At the moment he's a bit hesitant.
"You look at Eto'o tonight and he put a shift in for them and hit the bar, but it's still not what the other sides at the top have got.
"That's the only thing holding him back."