A fortnight after squandering a first-half lead against Leicester, the Blues blew a 2-0 half-time advantage against the Blades to be held to a 2-2 draw.
Tammy Abraham's first-half double had looked like giving Lampard a first home win in charge, but Callum Robinson's effort less than a minute after the restart and Kurt Zouma's 87th-minute own goal handed the Blades a deserved point.
Lampard, who has been forced to turn to youth this season owing to the club's transfer ban, named the youngest side in the club's Premier League history, with an average age of 24 years and 158 days.
He handed a first start to 21-year-old Fikayo Tomori and brought on 18-year-old former Rangers midfielder Gilmour for his debut.
But for all their youthful energy, their soft underbelly was exposed, though Lampard says the two are not related.
"I don't put that together and I couldn't care less that we had the youngest team in (Chelsea's) Premier League history," he said.
"It was a real plus last week. The fact that it is young today, I don't think it relates at all.
"The lack of concentration caused mistakes for the goals, but you defend as a team as much as attack.
"We concede because we switch off in a game we should be comfortably seeing out at 2-0 up. That's not disrespecting to Sheffield United, 2-0 is not the end of the story.
"I was clear with the players at half-time that it could 3-0 and be nice or a potential 2-2 on our hands so the disappointing fact is the first goal because that allowed it. We can only look at ourselves as a group."
Lampard defended his decision to bring on Scotland U21 cap Gilmour.
"It wasn't bold. (Mateo) Kovacic was on his haunches, obviously tired and Billy Gilmour is a midfield player I have got on the bench," he said.
"Other people can make what they want of that, but I wasn't trying to be clever, I was trying to see the game out.
"I have got faith in Billy I think he is going to have a big future, but we have any injury in midfield, with N'Golo (Kante) who is a good player. But we have a ban, the squad is what the squad is."