The Bantams, who won promotion via the League Two playoffs last season, travel to Bristol City on the opening day of the season.
Parkinson believes that his side will not be fazed by facing the Robins, who were playing in the Championship last season.
"Pre-season has gone well and we're all excited about the new campaign now. We're ready for action," he told Bradford's official website.
"We've got a great start. Bristol City away offers us a great challenge. The expectations will be on them to be right up there, having come down [from the Championship]. We can go there and express ourselves and feel our way into the division. We aren't going there to sit back and let them dictate the game to us.
"We've got a team of players who have played on big stages all through last season. I said at the time it would be a huge benefit for our players and I genuinely feel that going into this season."
The Bantams also reached the final of last season's Capital One Cup, where they were beaten by Swansea City.