It was a chastening result for new Chelsea manager Lampard after the club's record goal-scorer took over from Maurizio Sarri in the close-season.
Lampard suffered the heaviest defeat by a Chelsea boss in their first game since Danny Blanchflower lost 7-2 at Middlesbrough in December 1978.
Marcus Rashford put United ahead with a penalty after Chelsea had hit the post through Tammy Abraham.
Emerson also struck the woodwork before the interval, but Rashford, Anthony Martial and Daniel James netted after half-time to leave Lampard frustrated.
The manner of Chelsea's second half surrender will raise questions about former England midfielder Lampard, who has just one season of managerial experience at second tier Derby.
But he insisted the result was harsh on Chelsea because they controlled the game for long periods.
"Four mistakes for the goals, let's get that out straight away because we have to be self-critical about that," Lampard said.
"But other than that, for 60 minutes we controlled the game. It wasn't a 4-0 game for long periods but we need to accept it.
"At half-time we should be in the lead. Then all of a sudden the second and third goals, two mistakes, and it's much easier for them."
Chelsea were without injured stars Callum Hudson-Odoi and Antonio Rudiger, while France midfielder N'Golo Kante was only fit enough to come off the bench.
"At 1-0 we were the better team but I can't stand here and look happy with that because it's 4-0," Lampard said.
"We are missing internationals and big players but I don't want that to be an excuse."
In contrast to Lampard's woes, it was a dream United debut for England defender Harry Maguire.
Maguire became the world's most expensive defender when he moved to United from Leicester for £80 million days before the transfer deadline.
His presence immediately made a United defence that crumbled too often last season look more imposing and Maguire called on his team to turn Old TraffoRead More