Chelsea lost for the third straight game in Lampard's temporary spell in charge despite taking the lead against the Seagulls.
Conor Gallagher gave the hosts the lead at Stamford Bridge but Danny Welbeck equalised on the stroke of halftime and Julio Enciso struck a superb second half winner for the visitors.
Chelsea remain in eleventh position and are without a win in their last five Premier League games.
"I'm disappointed on every level," Lampard said after the game.
“The better team won. They could have won by more. They played like a team. They've been together a long time.
"[We were] not good enough. All the basic parts of football - to fight, to run - we were short on. [It's] not a question of commitment as such.
"Some players physically couldn't be able to play Wednesday, Saturday, Tuesday. Some of those changes were forced and some were opportunities. In a modern day squad, you have to be ready to come in.
"As a team, we were short today. Where can we get better quickly? For me, it's the football basics.”
Chelsea face a quick turnaround when they meet Real Madrid in the second leg of their Champions League quarterfinal tie at Stamford Bridge on Tuesday and Lampard has demanded a response from his men as they try to overturn a 2-0 deficit.
"There's no point being too down, but we have to understand why today went the way it did," he continued.
"In football, a story can change very quickly. Real Madrid in the Champions League is the pinnacle of football. There's things I'll say to the players that I'll keep in house.
"Chelsea fans will be coming on Tuesday to see a team give everything to turn it round, and that's what we have to do."
