The Blues finished sixth last season, their lowest finish in the Premier League for 10 years, after suffering a poor start to the campaign under Andre Villas-Boas.
Terry is determined to put that right this season and is eyeing up taking six points from their next two games against Reading and Newcastle.
"You definitely don't want to fall behind, which is what happened last season," he told the club's official website.
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"Once you've fallen six or seven points behind, you can't see the likes of Man City losing very often, and the same goes for United and Arsenal.
"You look at the strength-in-depth of squads such as ours and the two Manchester clubs, we probably have the three biggest squads, and that could be a key factor."
Terry feels his side must be on their guard when they play the Royals especially after the scare Southampton gave Manchester City at the weekend but is determined to get the three points to send the Blues to the top of the table.
"It was an interesting one, but I don't think you can take too much from the first few weeks," he added.
"Looking at the Manchester City game, people will probably have expected them to turn Southampton over easily, but sometimes these teams come up and show a bit of something that surprises teams.
"We saw that with Southampton and, in a way, it's a good thing because it ensures we have our backs up and we're ready for it.
"We're certainly not underestimating Reading. Being at home, we obviously want to come away with three points, but we realise it will be tough.
"They will probably have looked at this game and thought if they can get a point they'll be delighted.
"In the past, teams have come and sat back and made it difficult for us, but the new boys [Hazard and Oscar] looked sharp at the weekend and hopefully they can give us that new dimension."