"Well, he’s a young player, we’ve all done it… an interview after the game, you’re emotional, you’re not happy," said Giggs, who was working as a pundit for Optus Sport for the Manchester derby.
"I don’t know why he’s wearing that cap, but that might be just me – old school, not like the modern footballer now,"
Rashford played the match at Old Trafford, but could not help his side pick a point as they went down after goals from Leroy Sane and Bernado Silva.
Speaking after the match, the Englishman apologised to the fans, and urged his teammates to 'start playing like Manchester United'.
"I think on the pitch we need to support each other more, react better to mistakes, everything, the whole bunch of it needs to improve," said Rashford.
United face another tough fixture at home this Sunday, welcoming fourth-placed Chelsea FC in a crucial tie.