Jimmy Abdou silenced a full house at Elland Road on Thursday with a 73rd-minute equaliser as the second leg ended 1-1 on the night, clinching Millwall a 2-1 aggregate win and a date at Wembley against either Scunthorpe or MK Dons a week on Sunday.
Leeds striker Luciano Becchio had levelled the tie early in the second half, sending most in a crowd of 37,036 into raptures after the disappointment of seeing Jermaine Beckford's penalty saved five minutes earlier.
Lions boss Jackett said: "To overcome Leeds, who are a very good team, over two legs is a very good achievement.
"It was one of the best atmospheres here tonight that I've been involved in and when their goal went in, there was some momentum there and we came back from that very well.
"I've got to say the Leeds crowd were magnificent tonight. The atmosphere they built and then their singing at the end.
"Walking back myself, they were first class, congratulating us and although it's no consolation they were a credit to their club."
Millwall arrived in Leeds with a slender one-goal lead, courtesy of a solitary goal from Neil Harris in Saturday's first leg, and failed to crack under intense Leeds pressure and a super-charged atmosphere.
Jackett said: "There's no secret to our spirit. People look for secrets in football and there aren't any.
"There's honesty, hard work, commitment and at times quality.
"The start of the second half was really built up and I've got to say they had us under a lot of pressure."
Jackett, who spent his entire playing career at Watford, took charge at The Den in November 2007 with the club fourth from bottom of League One.
He was unaware the delay for Beckford's penalty had been because a coin had been thrown at his goalkeeper David Forde.
Jackett added: "Forde's head seemed all right to me afterwards.
"We've no preference who we play (in the final). We have to worry about ourselves, focus on it and make sure we're in the right mentality to go and do the job."