Lampard’s side fell behind to Ireland international, Michael Obafemi’s superbly taken strike at Stamford Bridge and had fewer shots than in any game since he took charge during the summer.
The introduction of Mason Mount for defender Kurt Zouma at the break injected some energy but only a vital Fikayo Tomori intervention denied the away side a second.
And with 20 minutes remaining, a fine team move saw the ball break for Nathan Redmond and his simple finish from 10 yards wrapped up six points for Ralph Hasenhuttl’s side from festive away games at Aston Villa and the Blues.
It means Chelsea have now lost five of their last seven league games and three times in a calendar month for the first time since 2015.
“We control a lot of the ball but we do not do enough with the ball around the box,” Lampard told BBC Radio 5 Live.
“I think it’s been the story for us for a while, not just in recent times. We need to get better because we need a better home record.
“What we need to do, the players on the pitch, whoever they are need to make goals and score goals. It’s the hardest thing to do in football. It’s a challenge for all of us.”