Terry skippered Jose Mourinho's Blues to a 1-0 victory over City at the Etihad on Monday night.
Branislav Ivanovic's solitary strike means the west London club are now well and truly in the hunt for Premier League honours, level with second-placed City and only two points behind Arsenal.
Former England defender Terry feels that the result could give other teams confidence against Manuel Pellegrini's side and further shake up the title race.
City failed to get on the scoresheet in a season that has so far seen them almost score at will.
"They've been phenomenal scoring goals and turning teams over," Terry told Sky Sports.
"It was important not just for us but for other teams, showing that they can be beaten."
Mourinho's methods have come in for criticism in the past but the Portuguese proved he knows how to set up a team to get a result, something which Terry hailed following the victory for the Blues.
When asked if the result told the story of a Mourinho masterclass, Terry said: "Very much so. This is where he comes into his own.
"We spent a couple of days working on their strengths and weaknesses.
"After the disappointment of dropping two points against West Ham, it was important to come here and bounce back.
"In the first 15 minutes, they were very good and made it difficult. We showed a lot of character. Overall, we were very solid and happy for the win."
I am no messenger, but I will give you a message. The message of death! (points available to anybody who knows where that's from)- tk421