Lampard's first competitive game at the helm of the Premier League club ended in a comprehensive loss at Old Trafford, where Marcus Rashford scored a brace to go with goals from Anthony Martial and Daniel James on Sunday.
Working for Sky Sports, former Chelsea boss Mourinho criticised Lampard's selection, saying more experienced players like N'Golo Kante, Marcos Alonso and Olivier Giroud should have started, while questioning the performances of Mason Mount, Tammy Abraham and Andreas Christensen.
⭐ THE SPECIAL ONE'S DEBUT— Sky Sports Premier League (@SkySportsPL) August 11, 2019
What a game to unveil @SkySports' star summer signing Jose Mourinho ✍️
On Super Sunday the legendary boss offered unique insight into both his former clubs, @ManUtd and @ChelseaFC - watch the best bits here!
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Lampard seemed surprised by Mourinho's comments, saying injuries had an impact on selection in his side's season opener.
"He didn't like the performance of Mason Mount? Is that what he said? Did he? Wow," he told a news conference.
"Well, I can't drag players out of the medical room to play if they are experienced or not, so these are the players that played in a game that we were clearly the better team for 45-60 minutes.
"What was evident that we made individual errors that led to four goals out of their five shots. So there's the harsh reality for us.
"I don't have to be too concerned about what anyone else says, pundit-wise or anyone, they have to speak. At the same time, what's clear is the squad is what we've got and I believe in it.
"If we go in at half-time 2-1 or 3-1 up, as we probably should have done if we were more clinical and maybe had a stroke of luck here and there, the game would've been completely different."