Fred surprisingly escaped a straight red card after the altercation with the PSG midfielder with Italian referee Daniele Orsato only brandishing a yellow after reviewing the incident on the VAR monitor.
However, the United midfielder was later sent off after picking up a harsh booking for a foul on Ander Herrera in the second half.
Fred escaped a red card after headbutting Paris Saint-Germain midfielder Leandro Paredes
Michael Owen claimed the midfielder does not deserve to play for Manchester United again
Owen had little sympathy for the Brazilian and also criticised Ole Gunnar Solskjaer for not taking him off at half-time.
‘Mistakes all round really,’ he told BT Sport.
‘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.
Owen described the Brazilian’s actions in the first half as as ‘petulant’ and ‘pathetic’
‘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.’
Fred was sent off a minute after United had gone 2-1 behind and his dismissal left his team-mates facing an uphill battle to get back into the game.
The French side went on to score a third in the 91st minute, leaving United needing a point from their final group game against RB Leipzig in order to progress to the knockout stages.
Solskjaer admitted Fred had been lucky to stay on the pitch after headbutting Paredes but insisted his tackle in the second half did not warrant a yellow card.
Fred (not pictured) was harshly sent off later on in the second half for a foul on Ander Herrera
‘I thought he was a bit lucky to stay on when the referee decided to give him anything,’ Solskjaer said.
‘Fred shouldn’t put his head towards him. I don’t think he touched him but you don’t so that. He was a bit lucky. It’s either nothing or red card.
‘We spoke about staying calm and staying your feet and the second yellow was nowhere near a foul – and Ander knows that as well.
‘It wasn’t a foul. Fred played really disciplined second half but when he makes a tackle light that you can’t fault the boy.’