Parkinson and assistant Steve Parkin were both sent to the stands for their part in a mass melee in a frenetic first period that saw Millwall defender Mark Beevers dismissed and the home side score three times as Bradford produced another cup upset at Valley Parade.
Parkinson and Parkin, whose side defied the odds two years ago to reach the Capital One Cup final, were ordered from the dug-out by referee James Adcock for remonstrating with Millwall defender Alan Dunne, whose challenge had sent Bradford striker James Hanson crashing into the advertising hoardings.
But after Billy Knott had added to goals from Hanson, Jon Stead and Andy Halliday to book a coveted fourth-round tie at Chelsea, Parkinson could not hide his delight.
He said: "There was a big prize at stake, to get the club into the fourth round for the first time in 15 years, so the tie at Stamford Bridge, we wanted to achieve that and we focused on the factors that would help us.
"I thought the lad that pushed James into the hoardings - I thought it was a dangerous challenge because there's a wall just behind them.
"Me and Steve reacted and ran down, as well as some of their staff, and the ref's decided to send me and Steve to the stands.
"I said to the lads at half-time I had to apologise for that because I had to ask them to keep their cool and stay on the pitch.
"But I'm glad it didn't ruin a great night
The lads didn't need us on the touchline anyway
It was nice and quiet for us in the stands."
Bradford will take on Chelsea on Saturday, January 24 and Parkinson is aware of the prestige surrounding a trip to the Premier League leaders and the subsequent cash windfall.
"I'm not sure (of) the amount but it will be worth a considerable amount of money when you look at it as a percentage of our overall budget," the former Colchester and Hull boss added.
"So we're pleased with that and we set out with a focus to get there
It makes things easier all round for the club like it did with the trip to Wembley two years ago."
Millwall defender Mark Beevers was shown a straight red card for hauling down Hanson in the sixth minute and the Londoners never recovered.
It was a forgettable night in a wretched season for Ian Holloway's side, FA Cup semi-finalists themselves two years ago.
They are third bottom in the Sky Bet Championship table, have now won only two of their last 22 matches and boss Ian Holloway kept his players in the dressing room after what was a fifth defeat from their last six matches.
Holloway accepted referee Adcock was left with no choice other than to send Beevers off and said he had never before seen a side of his fold like Millwall did
He did insist he would turn things round at the club.
"The lack of confidence in the team and in each other, we let a goal in almost straight away," Holloway said.
"You could see how bad it is for everybody and in all my time in football I've never seen a team capitulate as bad as that.
"All I can do is apologise to the fans
We've got so much work to do
The lads don't look like a Millwall team, they didn't have any fight in them, they don't look like my team.
"Well done to Bradford
To a man they looked like they wanted it more than my lot after the sending off."
Both Bradford and Millwall fans were chanting 'You're getting sacked in the morning' and Holloway admitted those words hurt.
"It's football at the moment isn't it? I've been doing it 19 years and 860-odd games and this is football at the moment," he added.
"I said it would be tough when I came here, but I didn't think it would be as tough as this."
Source : PA