Shane Long was the matchwinner in the Welsh capital as he bagged his 24th and 25th goals of the season, the second of which came from the spot, before Jobi McAnuff struck a late third to secure a convincing victory, with the tie goalless after the first leg at the Madejski Stadium.
McDermott said: "I've been to Wembley in 1978/79/80 with Arsenal and never played. I was at Oxford and never played when we won in 1986."
He added: "I missed out in an FA Trophy semi-final against Southport, I missed out to go to the semi-finals against Aston Villa and against Manchester City.
"So that's what it means to me. To go out there, walk out with the team, our supporters behind us, I'm just delighted for the staff, players and supporters."
Cardiff counterpart Dave Jones was left to rue two defensive gaffes which gave his side a mountain to climb at half-time, but he remained dignified in defeat.
Naturally, attention turned to Jones' future following the latest setback in his attempts to guide the club to the top flight after what is now a 49-year absence, coming 12 months after last May's dramatic 3-2 play-off final defeat to Blackpool.
And while he insists he still has the passion and drive, he admits his time in the Welsh capital is open to debate from both his side and that of the Cardiff board.
"At the moment I feel lower than a snake's belly," Jones said.
"I'll take stock of my life, my position and whether I want to (continue). And it's whether the owners and the hierarchy of the football club want you to."