Samuel Eto'o seized on a Jan Vertonghen error to open the scoring and Demba Ba added a late brace to Eden Hazard's penalty as the Blues saw off the challenge of their 10-man London rivals.
But Terry insisted Manuel Pellegrini's City, nine points behind but with three games in hand, were still in the box seat.
"City are the strongest side," he said. "and they've got games in hand. They've got a bigger and better squad. All we can do is keep winning our home games."
Cardiff City captain Steven Caulker led from the front with two goals as the Welsh club beat fellow strugglers Fulham 3-1.
The centre-back scored in either half to give the Bluebirds' battle against relegation a boost while increasing the woes of their bottom-of-the-table opponents.
Victory put them within a point of safety with West Brom, who lost 3-0 at home to Manchester United, the team immediately in their sights. United kept alive their slim hopes of a top-four finish with goals from Phil Jones, Wayne Rooney and substitute Danny Welbeck.
United remain nine points adrift of Man City, who occupy fourth spot but have two matches in hand over their neighbours.
Norwich edged four points clear of the drop zone with a 1-1 draw at home to Stoke, who had scorer Jon Walters sent off five minutes after hitting the equaliser.
Southampton consolidated their position in ninth place as Jay Rodriguez's breakaway in the 37th minute provided the only goal against Crystal Palace, who themselves are only two points above the bottom three.