Terry, 26, also firmly believes England have the talent and self-confidence to finally deliver on the big stage.
"I want to be a captain to be remembered - that means taking us to the Euros and really giving ourselves a chance to win something with England," declared Terry, who has been skipper of the national team for just over a year now.
"To be the captain and do that would be something amazing. We are a long way off at the minute, but hopefully the possibility is there."
"When I have not been involved in games, I have travelled to a lot of games and you see these supporters coming in from work, picking their kids up from school and coming to games in the evening."
The Chelsea defender recalled: "I was like that as a kid. My mum and dad saved up for tickets. I know exactly how much it means to them and exactly how much it means to everyone in England.
"When England play well it gives everyone a lift. We all know that.
"People go into work on Monday mornings very high after a good result, so it is key.
"We have said a lot of things too many times - but this is the crunch now and we need to let our football, our results and our performances do the talking.
"Russia are a very good side, it is going to be a very tough game - but if we can win again hopefully we can get the belief of not only the fans but of everyone in the country. Then we can all move on together."