The Bantams ended their six-year spell in the bottom tier with a one-sided 3-0 win over Northampton in Saturday's League Two play-off final at Wembley and Parkinson was quick to praise his backroom staff.
"When we put the staff together, I warned them we were going to have to work really hard," said Parkinson, who is waiting for Parkin and Allamby to agree their new deals before he puts pen to paper on his new contract.
"I said I'll drive you mad ringing up all the time.
"We'd have to go beyond the call of duty but we'd all get our rewards. You need that total commitment.
"There is no easy way unless you've got a massive budget bigger than anybody else in the division, whether you are a Premier League club or whatever. The majority of teams at this level are more or less on the same playing field.
"It's the staff who keep working to find the solutions to problems who ultimately become successful. And we've worked hard every single day.
"That's why I'd like to see that everybody signs contracts at the same time. I'd agreed mine ages ago with (joint-chairman) Julian Rhodes, but I want to see it all done together.
"Once we've had the celebrations this week, I'll sit down with Julian and (joint-chairman) Mark (Lawn) and hopefully we'll get that finished. I'd like to keep everybody together because that's important."