Fred, 27, was lucky to not receive a straight red in the first half when he appeared to thrust his head at PSG midfielder Leandro Paredes.
The Brazilian midfielder walked away with a yellow card from the incident, only to be sent off in the second half for his challenge on former United man Ander Herrera.
Owen pulled no punches towards Fred and insisted that the Brazil international's actions in his first-half incident with Leandro were "pathetic."
The 40-year-old pundit told BT Sport: "Mistakes all round really."
"It was a red card. There wasn't much [in the headbutt] but come on, you're a grown man. You don't have to do these petulant little things to put your team at risk.
"If I was a manager and one of my players did this, just pure petulance, then he wouldn't play for me again. It's pathetic really."
United boss Ole Gunnar Solskjaer admitted after the 3-1 defeat that Fred was "lucky" to escape a straight red in the first half.
"Fred shouldn't put his head towards him [Paredes]," he said.
"I don't think he touched him. He was a bit lucky to stay on."
The 47-year-old Norwegian defended his decision to keep Fred on the pitch, saying that he had spoken to the player about "staying calm and on your feet."
Speaking about his decision not to sub Fred off, Solskjaer explained: "Yeah... but Fred has played really well.
"We spoke about staying calm and on your feet. The second yellow card was nowhere near a foul. Ander [Herrera] knows that. He definitely knows."
United are now second in Group H and are level on points with both PSG and RB Leipzig.
The Red Devils will resume their Champions League campaign on 8th December when they travel away to RB Leipzig.
Featured Image Credit: BT Sport
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