Florent Malouda, Bolton old-boy Nicolas Anelka and Ramires - with his first goal for the champions - were also on target to give Chelsea a 4-0 win which closed the gap on leaders Manchester United to seven points.
Coming to the fore: Ramires (centre) and team-mates celebrate after Chelsea's final goal
Asked if Sir Alex Ferguson's side still have reason to fear Chelsea, Terry said: 'I think so. In the past we've never given up.
'United are getting the right results and a little bit of luck - maybe that will turn. We still have to play them twice and if we can back in it.'
Manager Carlo Ancelotti echoed Terry's comments saying: 'I think we're back in it. We've turned a corner and we are coming back to fight for everything. It's not easy to close the gap, but we will do everything to do it.'
Title warning: Terry insists Chelsea can catch United in race for the championship
Drogba revealed Ancelotti had told him to shoot on sight and the Ivory Coast striker responded with his 10th of the season.
The strike was clocked at 61.2mph from a distance of 33.6 yards, and he said: 'I think it was the best goal of the season. The manager said to me you have to shoot if you get the chance.'
This was Chelsea's eighth straight win at the Reebok without conceding a goal, and they extended their unbeaten run here stretching back more than 13 years.
Take that! Drogba netted Chelsea's first of the night, and his 10th of the season at Bolton
It left Bolton fans more subdued after an emotional pre-match tribute to club legend Nat Lofthouse who died earlier this month.
Manager Owen Coyle said: 'We're hurting after that. We never envisaged that outcome.'
Chelsea are hopeful of reaching agreement on the transfer of David Luiz despite Benfica asking for £30million on Monday. Chelsea's application for a work permit for the 23-year-old Brazil defender will be heard tomorrow and they have offered £25m plus a player.
Bolton 0 Chelsea 4: Carlo's boys back on song as Blues fire four past Wanderers Bolton 0 Chelsea 4 - the action from the Reebok Stadium as it happenedSky duo face axe! Calls for Gray and Keys to be sacked amidst more damning footage
Explore more:People: Alex Ferguson, John Terry, Didier Drogba, Nicolas Anelka, Owen Coyle, Carlo Ancelotti Places: Brazil