Garry Thompson had Valley Parade rocking when he volleyed home after 16 minutes.
When Vermaelen's spot-kick miss put the League Two outfit through, the vast majority of the 23,971 crowd - City's biggest for 50 years - started to party.
Parky roared: "I just want to enjoy this occasion.
"I want my players and our fans to savour every second of it as well.
"I'm sure they will once the enormity of their achievement sinks in."