Goals from Pedro, Gary Cahill, Eden Hazard and N'Golo Kante handed United boss Jose Mourinho his heaviest ever Premier League defeat on his first appearance back at Stamford Bridge since being sacked as Chelsea manager last December.
The defeat was also United's biggest in the league since losing 6-1 to Manchester City in 2011.
Several United players could be seen warmly embracing Chelsea players after the match and some swapped shirts.
Speaking after the match, United's all-time record appearance holder Giggs expressed his displeasure with the attitude shown by the players after a humiliating defeat against their rivals.
"You can get beat in a football match, but then when you're getting beat and you're swapping shirts – which is something I don't like, call me old fashioned," he was quoted as saying by the Daily Mirror.
"If you get beat 4-0, you congratulate the opposition, you thank the supporters and then you get off the pitch. You don't stand around on the pitch swapping shirts and laughing with the team that's just beat you."
Meanwhile, Chelsea boss Antonio Conte refuted suggestions that he tried to "humiliate" Mourinho during the win over Manchester United.
Mourinho exchanged heated words with Conte at the final whistle at Stamford Bridge, with Sky Sports reporting that the Portuguese coach was unhappy with Conte's attempts to encourage the home fans to make more noise with the score at 4-0.
Conte refused to divulge what Mourinho told him at the final whistle but insisted that his actions were not disrespectful.
"Nothing happened with Jose, especially as my behaviour seemed normal. I didn't make fun of anyone, as I always demand respect," the Italian coach was quoted as saying.
"If you want to cut the emotions, we can stay at home and I will change jobs. I did something absolutely normal. I didn't do anything to humiliate Mourinho."