Cesar Azpilicueta’s own goal and Bryan Mbeumo’s late strike condemned Lampard to his latest demoralising loss since replacing the sacked Graham Potter.
Chelsea have failed to score in six of their last seven games and are languishing in 11th place in the Premier League.
They have not won in any competition since March 11 at Leicester, a winless run that now stands at eight games.
Six of those eight winless matches have come at Stamford Bridge and Chelsea supporters let rip after losing to West London neighbours Brentford, who have traditionally been in their shadow but are now above them in the table.
“Absolutely the fans are going to be worried. If you’re a Chelsea fan, you’ve been used to 20 years of success, you’re used to it and you want it more,” Lampard said.
“I’ve got no problem with fans booing. I’m not sitting here to go against the fans and say don’t boo the players.”
Caretaker boss Lampard is only in charge until the end of the season, with reports that former Paris Saint Germain and Tottenham boss Mauricio Pochettino is close to being hired as the latest manager of owner Todd Boehly’s troubled 11-month reign.
Boehly has already axed Potter and Thomas Tuchel, leaving the squad in turmoil when Lampard returned for his second spell in charge.
Lampard, who said there was “nothing” to add on a potential Pochettino appointment, is adamant his players are committed to the cause despite accusations from fans about their lack of work ethic.
Facing Chelsea’s first finish outside the top 10 since 1996, Lampard added: “I’ll defend the players because they’re young lads who want to do well. Is there an issue with confidence? Yes. Is there an issue with the balance of the squad? Maybe yes.
“I’m not patronising everybody. When you’re in this moment with a lack of confidence, then it can be difficult to win a game. I’m not exonerating the players, far from it. I’m just supporting them.
“Are we dynamic enough in the final third? No. Have we been for a long time before I came here? No. Those things are not things that are going to turn overnight. We have to keep working.”
