The Stamford Bridge outfit finished four points behind champions Manchester City last term, with late-season defeats to Aston Villa, Crystal Palace and Sunderland proving costly.
"I was in tears over the Premier League last year, over throwing that away and not winning it," Terry said.
"That’s what I play for week in, week out. I’m never scared to show my emotions.
"I just want to win trophies, that’s what I’m born to do, it’s in me from when I was a kid. I just want to win games, whether that’s in the Premier League or the Champions League."
But Terry is confident Chelsea can claim the top honour in English football this season for the first time since 2010.
And he hailed the 2014 signings of Nemanja Matic, Cesc Fabregas and Diego Costa as crucial in Chelsea's progression.
"Those three signings are quality, all unbelievable players but big characters as well, on and off the pitch," Terry added.
"What I call real men, and players with great experience as well.
"Matic had to come to Portugal [with Benfica] and gain experience, but came back to Chelsea a completely different player and a man now.
"Cesc has been in England before so he knew what to expect, and you expect him to hit the ground running, which he’s done.
"With Diego we didn’t know. We’ve seen it before: some strikers take months and months. But he’s hit the ground running.
"Eight goals already is superb and it’s great for us. He’s a good character, a great character. Without speaking a word of English he gets by and gets on great with everyone.
"He puts himself about but gets up and battles on, and plays with little niggles. That’s what you want. That’s why he’s come to the Premier League: to win.
"He made that clear to everyone in pre-season. He’s come here to win trophies. That’s what he wants to do."
