Terry sat within inches of the silverware on Thursday and admitted he had still not got over Chelsea surrendering it to United last season.
But the Blues captain insisted that made him more determined than ever to get his hands on the title when the season gets under way this weekend.
Chelsea went close to completing the greatest comeback in Premier League history last term but came up short as United were crowned English champions for a record 19th time.
However, Terry was confident history would not repeat itself this season.
"We can catch Manchester United," said the defender, speaking at the official launch of the 20th Premier League season.
"They have been the benchmark for 20 years.
"We pushed them to the end last season but missed out.
"We all see their quality and the hunger they have and that the manager has too.
"It really drives me on and seeing them lift the trophy last year still hurts to this day.
"I want to get my hands back on it and lift it.
"The competition is improving every year. The players are getting stronger and the managers want it even more."
Terry will lead the deposed champions out at Stoke on Sunday for the first competitive game of the Andre Villas-Boas era.
The new Chelsea boss has already made a big impression on his players, masterminding a pre-season campaign that ended with a 100% record.
That is in stark contrast to a year ago, when they lost all but one of their warm-up matches.
"The new manager has been great since he came in," said England captain Terry, who has already lifted the Barclays Asia Trophy this summer.
"We had a great tour of Asia with all our games won. When Andre came in, he stressed the importance of winning.
"We only won one game last pre-season. That wasn't the best of starts.
"But he's come in and drummed it in to us from day one.
"Andre has brought in new and fresh ideas that will hopefully help us win this (trophy) at the end of the season."
Villas-Boas is no stranger to Terry and many of his team-mates, having worked as a scout under Jose Mourinho at Chelsea and Inter Milan before striking out on his own at Porto, where he swept the board last season.
Terry added: "He's got an emphasis and demeanour about him.
"A lot of the lads knew him from when he worked here with Jose but he's gone away and done his own thing and we give him a lot of respect.
"We have to treat him as his own man. He has obviously learned from the best.
"He has brought an awful lot to us in a very short space of time. We are ready for the season."
Chelsea are not the only club looking to topple United, with many of their rivals having spent big this summer.
Terry said: "I'm worried about a lot of teams this season. Everyone has strengthened.
"Manchester City and Manchester United have bought in some good players, Liverpool seemed to have strengthened a lot.
"There are six or seven teams who can really push and have a chance of winning the trophy."
Chelsea were on the wrong end of some shock results last term and Terry admitted Sunday's game at Stoke could not be another.
He said: "It's not the easiest of starts. They have a great side and a great manager.
"If we want to lift this (trophy), we have to go there and win."
Villas-Boas' team selection at the Britannia Stadium will be eagerly anticipated, particularly whether he decides to play Fernando Torres, Didier Drogba or both.
Torres was forced off during Spain's friendly defeat in Italy on Wednesday night, reportedly after suffering mild concussion.
Chelsea confirmed on Thursday afternoon that they were monitoring Torres' progress with a view to his availability on Sunday.
Chelsea are on the brink of signing another striker in Anderlecht's teenage sensation Romelu Lukaku.
But the Belgium star will not be officially unveiled this week.
A statement on his official website read: "Please note that no official presentation and no press conference will take place in Chelsea this week."
Lukaku trained with his prospective new team-mates at the club's training ground on Thursday.
The Blues are now being linked with Dnipro's Ghana defender Samuel Inkoom, who told skysports.com: "To be honest, the day I heard Chelsea were interested in me, I was very happy.
"Who would not like to be linked with such a big club, with world-class players?
"It is a dream club for any player, specifically for young African players like me. Hopefully it will happen."