The East of Scotland Football League first division conference A side won the tie on penalties, after drawing 4-4 in a topsy-turvy affair at Volunteer Park.
Goalkeeper David Kane was the hero, saving two spot-kicks in the shoot to ensure the Pace will take on Livingston United next Wednesday night in the semi-final.
On the match, Smith said: “I felt that in the first-half, despite going a goal up, we didn’t actually play that well and we played right into Armadale’s hands. We sat too deep and conceded two really sloppy goals close together.
“After the break we deserved to go ahead but if we had a wee bit more of a clinical edge and composure in the final third we would have sealed up the game.
“Fair play to Armadale they really fought to get back into the match and then we go down to ten men and it looks like there will be only one winner, them.
“It’s not the only time our guys have went to extra-time this season with a man less and came through the tie.
“I have to give great credit to the players for the character shown but we made it hard for ourselves.”
Dunipace’s chances of trophy this season were all but gone with moments to go, after conceding a penalty in extra-time and being a goal down until the 120th minute, when captain Danny Ashe headed home from close range after a series of corners.
The boss praised his side's mentality and resolve, saying the group he has is one he wants to keep for next campaign.
“We took three excellent penalty kicks and just the way it went with the ten players giving everything for that final 30 minutes, I never felt like we would lose the shoot-out,” he explained.
“Our players were just so confident after seeing that really difficult period through and they played the penalties perfectly.
“David Kane made two great saves and I had complete faith in him.”Getting through was all that mattered tonight and we did that, but it could have been much easier.”