An own goal from Sweden's Daniel Majstorovic was enough to secure Terry's side the victory at a half-full Wembley.
"No chance," he told ITV1. "I would never step down. It (being England captain) is something I dreamed of as a boy.
"When I was four or five years old I used to watch England games and it's something I dreamed of being. I worked very hard to get here. I'm very passionate, very confident being England captain and very proud to be, also.
"It's a great achievement, walking the side out, and I'm very proud to do that."
Terry said of the Wembley crowd on Tuesday: "I said yesterday the England fans have always been great with me and the players, they are always behind us win, lose or draw. They get upset at times - like we all do - we're very passionate and that's what makes us the very best.
"We've got a great set of fans, and some great performances at the moment, so if we can keep that momentum for the next six months then hopefully things will be a lot better."