Goals from Pedro Rodriguez, after 30 seconds, Gary Cahill, Eden Hazard and N'Golo Kante condemned Mourinho to his heaviest defeat since Real Madrid's 5-0 demolition by Barcelona in November 2010.
It left United seventh in the Premier League table, five points below Chelsea, who climbed to fourth, and six points behind leaders Manchester City, Arsenal and Liverpool.
"You come with a strategy. You cannot concede a goal in the way we did," Mourinho told Sky Sports at Stamford Bridge.
"We were coming to have an offensive approach. We wanted to create chances. We showed that after the 1-0.
"The second and the third were counter-attack goals. If we score a goal like we almost did for 2-1, the game would be different.
"It is one of those days when you give the advantage to opponents by doing nothing.
"We made incredible defensive mistakes, individual mistakes, and you pay for that."
After the final whistle a stern-faced Mourinho whispered into the ear of his opposite number Antonio Conte for some time before stalking down the tunnel.
Conte had exhorted the home fans to make more noise after Kante scored Chelsea's fourth goal in the 70th minute.
But Mourinho refused to reveal what he had said to the Italian: "My words with Antonio Conte were for him, not for you."
Mourinho was appointed by United in May after being sacked by Chelsea owner Roman Abramovich for a second time last December.
He won three Premier League titles, three League Cups and one FA Cup over his two spells with Chelsea – 2004-2007 and 2013-2015 – making him the London club's most successful manager.
Explaining his antics, Conte said: "I was listening to the support of Manchester United, always supporting their team, and I was asking my team to do a clap for my players.
"All the players deserves this clap."
Pedro stuck within seconds of kick-off, sneaking in behind Chris Smalling to gather Marcos Alonso's pass and rounding United goalkeeper David de Gea to score.
After Cahill had made it 2-0 from close range in the 21st minute, Hazard and Kante got on the score-sheet in the second half.
Hazard bent a shot into the bottom-right corner from Nemanja Matic's pass before Kante strolled through the beleaguered United defence to roll in his first Chelsea goal.
"I am pleased with the performance," Conte said.
"We started well, moved the ball quickly, created chances to score the goal. I see the commitment in training and the players deserve this.
"We are improving. We must continue to work. Only through the work we can improve."
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