The Bantams, back in the third tier for the first time in seven years, climbed into sixth place after the weekend win over Sheffield United, but Parkinson said it is too early to set any targets for his side.
"We feel we've got a decent squad, but who knows at this stage how we're going to fair?" Parkinson told Press Association Sport.
"We've got a good spirit in the camp, we've got some good quality players, we've got a good mentality, but we've come into a new division and we're still in the very early stages.
"We're still in the relative unknown. There's a whole batch of teams this season who you see challenging at the top end.
"Last year when you looked at this division it was difficult to pick out, but this year there's a list of teams who potentially could be up there, Wolves obviously, Bristol City, Sheffield United, Peterborough, Preston.
"There's some big clubs this season, it's a great division to be involved in and we're going to enjoy the challenge."