Chelsea have won one Premier League title since Jose Mourinho's departure in September 2007 - when Carlo Ancelotti led the Blues to a league and FA Cup double in 2009/10 - and were out of contention by Christmas in the last two seasons.
The Blues were 11 points behind last Christmas, but after Monday night's goalless draw at Arsenal are fourth, two points behind Liverpool, who visit Stamford Bridge on Sunday and lead the Gunners on goal difference.
"The point still keeps us up there and amongst everyone," Terry told Chelsea TV.
"We all know - and the fans have seen it home and away - that we can get better.
"So whilst everyone is dropping points around us, hopefully in the new year we have to start firing and put ourselves on a good run of games.
"If we do that we're more than capable of pulling away from everyone."
Mourinho called for a raucous backing from the Blues faithful when Swansea and then Liverpool visit in quick succession on Thursday and Sunday, with Chelsea firmly in title contention.
"I hope Stamford Bridge is there for us; Stamford Bridge with noise," he added.
"On the last Boxing Day Chelsea were 11 points behind the leader, out of the title race. And we are there. Two points behind both leaders.
"We are there so we have reasons to keep going. The way to get the first objective, which is top four and Champions League - which will be hard for everybody - is to be close in the title race.
"Let's enjoy the moment."
Chelsea showed a steeliness reminiscent of Mourinho's first team at the Emirates Stadium to frustrate Arsenal.
Prior to the match at Arsenal, the Portuguese spoke of building a new dynasty after leaving a lasting legacy from his first spell.
Yet, ever the perfectionist, Mourinho demands continual improvement, particularly in front of goal.
"We are building a team not for one season, we are building a team for more than one season, the same way 2004/05 we build a certain profile of team, that was the profile of team that was Chelsea's base for almost one decade," Mourinho added.
"In this moment we are building another team with different people, with different qualities and with a different profile.
"If we score goals in a direct relation with what we produce, we would be in a fantastic situation, because we are not scoring enough goals.
"It's not just a problem of the strikers not scoring goals, it's also a problem of the other people don't transform half-chances to chances and goals."
Chelsea's defence has also come under scrutiny in recent weeks and Terry was pleased with just a second clean sheet in 12 league games.
"A lot of people have been speculating about us conceding too many," Terry added.
"I think we're third in the league in conceding (the fewest) goals and we've had a couple of games where we've conceded far too many than we're used to, but overall we've been very solid defensively."
Mourinho is still to be beaten at Stamford Bridge after 68 home league games as Chelsea manager and Terry hopes the Blues will show their class in the coming days to extend the record.
Terry said: "We've been great, ever since the manager was first here a long time ago. We've held on to that and it (Mourinho's record) means an awful lot to us.
"A couple of (home) games we've conceded early goals, which has probably given us a kick up the backside earlier than we would've wanted to.
"(But) we seem to be more flamboyant at home and at it, which is what you expect and what people want to see.
"We're very confident at home and we score a lot of goals at home."
Terry could be rested for the Swansea fixture with Liverpool in mind, but, fitness permitting, he will make his 600th Chelsea appearance in the coming days.