The Bantams triumphed in the play-off final last May having squeezed into the top seven following just one defeat in their last nine league matches, but Parkinson's plan to recruit League One players two summers ago appears to be paying off.
Asked if his players had so far exceeded expectation, Parkinson said: "No not really.
"We had a meeting with the players a couple of weeks ago and we talked about people saying how well we've done and what a good start it has been.
"But I expected us to in a way. When we were in League Two we signed a lot of players who I was confident could move forward with the club.
"That was the strategy we put in place then, myself, the chairman and (assistant) Steve Parkin. We didn't want a scenario where if we were to get promoted to League One we had to completely change the squad again.
"We tried to bring players in who were comfortable at this next level and so far we've shown that."
Bradford sit fifth in the table and will look to extend their unbeaten league run to seven matches at Walsall on Saturday.
"I think we can keep improving," Parkinson added. "As individuals and as a group, in all aspects.
"We're in a division where teams and managers do more homework on you, they've got more resources in terms of IT to watch your games and scouting networks.
"These details are ever more important at this next level and the research goes up as you go up a level, so we've got to keep evolving and improving as a team."