The Bees jumped to a 2-0 lead thanks to Igor Thiago's brace before Benjamin Sesko scored his first goal for United just before halftime.
After the break, Bruno Fernandes had a chance to level from the spot after Bryan Mbeumo won a penalty. But the United captain's effort was saved by Bees goalkeeper Caiomhin Kelleher. The hosts completed the 3-1 scoreline through Mathias Jensen.
Amorim later said: "Of course we want to win. We didn't control the game. We played the game of Brentford. First balls, second balls, set pieces. All the crucial moments were against us. Tough to lose again but we need to think about the next one.
"The first goal was a long ball. We worked on that in the week, and on set pieces. We knew the long balls (were coming) and one touch they had the opportunity. We need to do better.
"We didn't play our game. We only had control for some moments. But it was more or less all the same. We need to play our games, not the opponents, but they were stronger on that."
On his future as United manager after this defeat, Amorim added: "It is always the same to lose at this club, it hurts a lot. We need to think about the next one."