The Bantams, who triumphed in last season's League Two playoff final, currently sit fifth in the table having lost just one of their opening nine matches.
Parkinson has claimed that his policy of recruiting experienced League One players has paid off.
"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," TEAMtalk quotes Parkinson as saying.
"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 face Walsall on Saturday.