Saturday’s 1-0 win against Mansfield Town at The Racecourse keeps Wrexham third in the table, four points behind leaders Wycombe Wanderers.
With 28 points from the opening 14 games, Parkinson’s back-to-back promotion winners have quickly adapted to life at a higher level.
But with only a third of the season gone, the Reds’ boss believes there are a lot of clubs capable of challenging for a top-six finish.
“It is very difficult to predict at the moment,” said Parkinson.
“Barnsley winning on Friday and suddenly appearing fourth, there are teams all the way down to 14th who you think could be up there.
“People may say Wycombe are a surprise package but they are a team who have been in the Championship not that long ago and are always up there in this division so are they a surprise package? I am not sure.
“There are so many teams who will be fancying their chances.
“It is still early in the season, we have just got to keep our heads down and concentrate on what we have got to do.”
Wrexham got the better of Mansfield who clinched automatic promotion from League Two last term along with the Reds and Stockport County.
All three teams who came up are currently in the top-seven and Parkinson, who takes his side to Stockport this Saturday, explained why they have all adapted well to the step-up.
“That momentum is important,” he added.
“I feel that teams, particularly at home when you have got the crowd right behind them like we have, it helps and that has shown with the games we have had so far at home with just two points dropped against Huddersfield.
“I always watch everyone else’s recruitment and Mansfield are a bit like us; they have let some key players go who have done well for them and brought some quality in.
“Getting the balance of that right is absolutely key because we have come into a very competitive division and at the moment we are doing well.”
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