Following a roaring start to the contest in front of a vocal home crowd, City were three goals up before half time and on their way to an eventual convincing 4-0 victory over Ian Holloway's beleaguered Lions.
Parkinson said: "After the disappointment of Saturday (Rochdale) when we didn't get what we deserved, we have responded terrifically tonight (Wednesday).
"The way we started the game was magnificent and we did everything right throughout the night really - we were very professional.
"We set out to begin the game like we did down at Millwall in the first leg. We wanted to get at them early and try to stamp our authority on the match.
"That was the aim from the first whistle, and to score seven goals against a Championship side over the course of two games is a great tribute to our lads.
"Even at three-nil up, we kept doing the right things because we wanted to finish the game off and collect a clean sheet as well.
"Obviously there was a lot at stake tonight. Getting the club to the fourth round for the first time in fifteen years and the tie at Stamford Bridge against Chelsea.
"We wanted to achieve those things really badly and we focused on the things we needed to do right to get the job done.
"We have an important league game at Yeovil Town beforehand, but we'll go to Chelsea in good spirits and look to embrace the occasion."
Following City's successful #bethedifference promotional campaign, nearly over eleven thousand City supporters turned out to cheer Parkinson's men onto victory.
Parkinson added: "It was a great turn out from the fans and they made a great atmosphere.
"The staff deserve credit as well for getting the game on with the snow that was around on Tuesday, and for pushing this game to get that many fans into the stadium. The commercial guys and the staff in the ticket office deserve enormous credit for that.
"It was another great atmosphere here under the lights at the Coral Windows Stadium and they (the crowd) did make a difference.
"We've had a number of good cup nights here over the years, it is nice this time to give the fans one in the F.A Cup."
The only slight sour note of the whole evening from a Bantams point of view came on the half hour mark when Parkinson and assistant Steve Parkin were sent to the stands following a melee which broke out on the touchline after Millwall defender Alan Dunne had needlessly pushed James Hanson into the sponsor hoardings.
Parkinson continued: "Alan Dunne has pushed James Hanson into the advertising hoardings and he could have caused him an injury. It was a dangerous challenge because there is a wall just behind those hoardings.
"Me and Steve (Parkin) have reacted and ran down, as have a few of their (Millwall's) staff, and the ref has decided to sent me and Steve to the stands.
"I said to the lads at half time that I have to apologise for that because we had asked the boys to keep their cool tonight and stay on the pitch and, in the heat of the moment, I've reacted to what I thought was a dangerous challenge.
"You can get a yellow card for trying to injury an opposing player but me and Steve have been sent to the stands. We will take in on the chin though, and I'm glad it hasn't ruined a great night."