Kennedy, who signed a two-year deal with the Bantams in July following the expiry of his contract at Rochdale, made his competitive debut in last week's League Cup defeat at Huddersfield, but watched Saturday's 4-0 thrashing of Carlisle from the stands after making way for Ricky Ravenhill.
"I left Ricky out last weekend (at Bristol City) and I just flipped it around," Parkinson said. "I didn't need two (central) midfield players on the bench.
"Jason has been terrific for us though, he's a really good player. Not only is he unlucky not to be on the bench, he's unlucky not to be in the starting XI.
"I think he is going to be an immense player for us. The players who have come in, like Jason, have to push the lads who are in the starting XI at the moment out of the team.
"Competition within a squad is great and we know that throughout the season we are going to need everyone."
- Sports & Recreation