The 19-year-old defender joined on loan from Newcastle last Thursday but was not included in the matchday squad.
Fellow new signing Blair Turgott was named in the 18-man squad but was not called upon.
"He had a bit of fatigue from some training and I didn't feel confident putting him on the bench," Parkinson told BBC Radio Leeds.
"I hope he'll be a good addition because he's a very good player.
"I felt it was best to leave him for now so that he is prepared and ready to go next week."