The young centre-back was taken off at half time against Istanbul Basaksehir when he was on a yellow card.
Solskjaer defended the decision, saying Tuanzebe was on a yellow card and his team needed to be aggressive in chasing a 2-1 deficit.
Parker told Eurosport: "I am worried about Tuanzebe and how he has been treated by Ole Gunnar Solskjaer. He had a great game against Paris Saint-Germain, then had no involvement until the next Champions League game.
"He got another opportunity last night and then got dragged off. I'd be concerned about how that will affect him mentally. He might wonder why he was subbed when he wasn't at fault for the goal, and be looking at the £80 million captain alongside him.
"Taking Tuanzebe off could be a mammoth mistake in the long term."