The 19-year-old appeared to be stamped on by David Meyler during Tuesday's 3-1 win over Hull City at Old Trafford, with the interim boss calling for retrospective action
Januzaj appeared to be deliberately stood on by Hull midfielder David Meyler in an unsavoury incident during United's 3-1 win at Old Trafford, leaving the attacking midfielder with visible marks on his leg.
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"I didn't see it, but I've seen his leg [with stud marks]," Giggs told reporters after the match.
"It's not great to see, it is terrible his leg. He needs protecting, he's a brilliant player, he's exciting, the authorities need to stamp down on it.
"I'm not sure what can happen now but it was bad, I didn't see the stamping but I've seen his leg and it's a joke. It's not broke the skin but it just goes from knee to his ankle."
It is not the first time Januzaj has been the victim of a stamping incident, with Fulham defender Sascha Riether suspended for three games after the FA used trial by video to punish the German.
Meanwhile, Giggs's playing future remains uncertain after the Welshman confirmed he would take time to think about the situation at the end of the season.
The 40-year-old, who is out of contract in the off-season, was a second-half substitute in what could have been his final home appearance for United.
With Louis van Gaal expected to take the reins in Manchester, Giggs is in contention to join the Dutchman's backroom staff but his days as a player are still up in the air.
"Not decided yet, nothing's changed, just wait till the season's finished, get a holiday and then think about it in the next couple of weeks," he said.