Villa secured a 1-0 victory on aggregate over Middlesbrough to progress to the final. The match held a minute's applause ahead of kick-off for former defender Jlloyd Samuel who was killed in a car accident on Tuesday.
Terry told 'Sky Sports': ''It's unbelievable and incredible. The support from the lads, the dressing room is incredible. There is a great team spirit among the boys. One more step and it'll be the dream."
''It was quite tense, I think our game plan worked superbly so our manager deserves a lot of credit for that. The boys have been superb and we're off to Wembley - one more to go. We'll not get too excited, there's still one to go. It's a huge week ahead for us.''
Villa manager Steve Bruce, who was responsible for Terry's signing, praised his side for turning their luck around after he took the reins shortly following their relegation in 2016.
Bruce said: ''Eighteen or 19 months ago this club was in a mess but the experienced players have done the job for us and we're delighted about that.''
''As a one-off, it's fantastic if you go up through the play-offs, although I would love to have been second and sitting on a beach now. ''