Four first half goals from the home side in the first 35 minutes became insurmountable for the Red Devils as they started the 2022/2023 season with back-to-back defeats.
De Gea was at fault for Brentford's first two goals; allowing Josh Dasilva's tame long range effort to evade his grasp before his pass to Christian Eriksen was intercepted for Mathias Jensen to score the hosts' second on 18 minutes.
Ben Mee and Bryan Mbuemo completed the rout to give Erik Ten Hag an imperfect welcome to the Premier League as Manchester United manager.
De Gea reckoned his role in the defeat and duly owned up after the game.
"I cost three points to my team today, to be honest," De Gea told Sky Sports.
"It was a poor performance from myself. After the first mistake and the second, it was very tough for the team to get playing. It was a horrible day.
"We should react better. I should save the first shot and probably the result would be different. It just depends on how the game is going, sometimes I maybe have to read the game better and go long [for the second goal].
"I tried to play when I shouldn't have to Christian. We are not like other teams conceding first and winning 5-1 or 6-1. This is why I cost the team three points
"It was an easy save. We have to react much better and be capable of scoring goals. It was a poor performance. It's easy to play in pre-season when you play for nothing.
"When you play the games that matter, you need bravery and to be proper players. That wasn't the case. We have to keep working, head up, it is the beginning under a new manager and a lot to improve."
Manchester United will welcome Liverpool to Old Trafford in their next Premier League outing.
