The Red Devils slumped to the bottom of the Premier League table for the first time since 1992 after enduring an almighty collapse in the capital.
Manager Erik ten Hag questioned his players' hunger and shifted the blame on individual errors as the Dutchman became the first United manager in 100 years to lose his first two games in charge.
De Gea, who endured a nightmare first-half against the Bees, fronted up to the TV cameras to apologise for his errors.
He later spoke with the club's website, and said: "It's difficult to be honest," said the Spaniard. "It's still tough moments. I say this many times, but I know the lads, and everyone is working hard.
"I'm working hard, the manager's working really hard, so that's the beginning.
"We made a big change so these are just the first games. We need to improve a lot, listen to what the manager wants and of course start to win games.
"It doesn't matter who we play against. We need to prepare for the game very well. We have a long week.
"It's going to be tough of course, after this defeat. But let's put our lives in training, put our lives on the games, and let's play for the badge and our pride."
Manchester United turn their attention to Liverpool next weekend as they welcome Jurgen Klopp's Reds to Old Trafford