The Bantams crowned a memorable season by securing their first promotion since reaching the top flight 14 years ago, three months after their historic Wembley appearance in the final of the Capital One Cup.
Parkinson's side stunned Bradford-born Aidy Boothroyd's Northampton with three goals inside the first 28 minutes from James Hanson, Rory McArdle and Nahki Wells to end a 64-game season on a glorious high.
But when asked if his side would now chase back-to-back promotions, Parkinson said: "You've got to be careful before you go shouting from the rooftops. When we've settled down we'll discuss what budget we're going to have to go forward with next season and see how we can do.
"But whatever budget and players we have, one thing Bradford City is now known for is that we have a group of players who give their all and we'll do that again next year."
Parkinson, 45, confirmed he had verbally agreed a new contract with the club "ages ago", but was waiting to sign it at the same time as assistant Steve Parkin and fitness coach Nick Allamby, whose deals were still in the process of being completed.
"When we've had the celebrations this week I'll sit down with (joint-chairmen) Julian (Rhodes) and Mark (Lawn) and hopefully we'll get that finished."
Bradford were taught a football lesson by Swansea in a one-sided Capital One Cup final, but Parkinson felt the chastening experience had helped his players settle quicker than their opponents.
"Without a shadow of doubt," he said. "It gave us the experience of being here before, not just here but the build-up to the game, the extra press attention, the new suits, the ticket demands, how your family are going to get down, your wife's new outfit, your kids' new outfits, it can drain a lot of energy out of you.
"We took all that away from the lads this time. We said we were here to do a job to finish the season off in style. It certainly benefited us to just come in this time and get the job done."