Chelsea are still in the FA Cup and Europa League.
Terry told the Sunday Mirror: "Managers will come and go. Players will come and go. But we must give these fans something to cheer for and to fight for. We are through in the Europa League, we are still in the FA Cup. The Premier League, realistically, we don't have a chance of that, but we will fight for the Champions League spots because we know how much it means to the owner and to the fans. They are the most important thing.
"We have not really been playing too well all season. So we know we have another level to go to.
"With everyone in front of us, we are quite encouraged that if we put on a good run, if we put in some good form, we can pick up some points and catch the teams above us.
"That's the target - to make the Champions League next year, which is a must for us.
"We have got a big derby now and we have to aim to just keep winning games and putting on the pressure.
"We are mentally very strong. We have dealt with ups and downs throughout season after season, we will always remain together.
"When you go 2-0 down at Man United, then you see the real team spirit. Nine times out of 10 other teams would chuck the towel in.
"We went the other way and we kicked on and absolutely went for it. People like David Luiz were excellent and really took the game by the scruff of the neck. That's what you want to see."