The Blues dominated the opening 15 minutes of the heavyweight clash at Old Trafford, before Kurt Zouma's clumsy challenge on Marcus Rashford allowed the England striker to open the scoring from the penalty spot.
Chelsea reacted well and pressed hard for an equaliser, seeing the majority of the ball throughout the match, but Anthony Martial doubled the hosts' advantage after 65 minutes.
Rashford grabbed a second two minutes later as the visitors began to open up in the middle of the pitch, before substitute Daniel James completed the scoring with a debut goal late on.
Lampard opted to leave Olivier Giroud and £58 million ($70m) signing Christian Pulisic on the bench, with Mason Mount handed his first competitive start for the Blues and Tammy Abraham tasked with leading the line.
Former Chelsea and Manchester United boss Jose Mourinho told Sky Sports after the match that Lampard's side were "too soft" in their approach, but Melchiot has refused to condemn the 41-year-old's tactics.
“I thought they started the game really well," the ex-Chelsea star told Talk Sport on Monday morning.
“When you go to Old Trafford it’s always tricky, but I felt Chelsea were in control in the first 15 or 20 minutes.
“Of course, when the penalty happens, it changed the whole game.
“It’s too early in the season to start talking.
“The only bad thing for Frank is the big games come so quick [Chelsea next play Liverpool in the UEFA Super Cup on Wednesday].”
Melchiot pointed to that moment as proof of the midfielder's lack of experience, but hopes Lampard will be able to keep the younger members of his squad motivated in the weeks to come.
“You look at Mount – he had two opportunities to strike the ball and it was purely down to experience, he was thinking too long," he added.
“Sometimes too much time in the box is not a good thing, because you’re in two minds. He had two opportunities and he tried to square it instead of putting his foot through the ball.
“But hopefully Frank can keep the young boys motivated and he doesn’t let their heads drop too early.”
Next up for Chelsea is a UEFA Super Cup date against Liverpool in Istanbul on Wednesday, before their first home game of the new Premier League season against Leicester four days later.