Darmian finally got his wish to leave United after several seasons on the periphery of the first team.
He joined Parma in a permanent deal on deadline day.
While he praised Louis van Gaal and Jose Mourinho for improving him as a player, he did not have similar words for Solskjaer.
"Van Gaal and Mourinho are two great coaches, they have won a lot, you know them," Darmian said to reporters.
"They are two great coaches who have left me something positive and I thank them."