Michael Keane and Dominic Calvert-Lewin had Everton 2-0 ahead, but Brentford stormed to a 2-3 win with three goals in the final nine minutes via Antoine Semenyo, Lewis Cook and Luis Sinisterra.
Dyche said, "We did so much right until they scored their first goal. I think they had one shot on target before then. The game should have been out of sight. We conceded one and then threw it away. I can't put my finger on it right now.
"They kept raining it forward and got their reward in the end. The Premier League you have to play to the last breath of the game and we simply didn't but they did. They were playing it forward and crossing it into the box and we didn't deal with it. Simple stuff but we threw it away. It is the third game we have thrown away this season.
"You have to kill teams off at every level, but particularly at this level. Everyone was looking at someone else to deal with things and that is when there is trouble. You could see the body language change.
"You have to see games through and we have enough experience to do that, but today we didn't."