The Warriors, who will face defending champions Leinster in the showpiece final at the RDS on May 31, had lost for the last two years at the semi-final stage.
But on Friday night they gave everything to secure a narrow 16-15 win over Irish rivals Munster and book a spot in the final.
And Seymour insisted that the support of a 10,000 strong sell-out home crowd had made all the difference as the Gregor Townsend's men secured a ninth successive victory.
He said: "It was unbelievably tense. When we scored our try and managed to get a nine-point lead we were looking good.
"But Munster did what they've been doing all season and came back strongly. It made the last 15 minutes agony.
"The last few minutes were unbelievable but we had our guys putting their bodies on the line.
"Some of the tackles were incredible as we had boys smashing into Munster at the end of what was easily the hardest game of our season.
"What a feeling it was to do that in front of a packed home crowd.
"They really pushed us over the line as I don't believe we could have performed like that if It hadn't been for them.
"This is an unbelievable team to be a part of and the supporters have been incredible."
Follow us on Facebook, join the conversation on Twitter, sign up to ourYouTube channel for extensive match highlights and sign up for ournewsletter for regular updates on the RaboDirect PRO12.
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland