It was a first half with few chances for either side but Brentford took the lead after 34 minutes through Fabio Carvalho to lead at the break.
The visitors were happy to sit and let Bournemouth have the majority of possession, but they struck for the second time after 65 minutes, Igor Thiago finishing a rapid break after the Cherries gave the ball away on halfway.
The Cherries weren’t able to breach the Brentford defence, and, after Julian Araujo was sent off for a second bookable offence in stoppage time, they were knocked out of the cup.
Andoni Iraola made eight changes from the side which beat Wolves, handing first starts in a Cherries shirt to Amine Adli, Eli Junior Kroupi and Ben Gannon-Doak.
Justin Kluivert and Ryan Christie were also included in the starting XI, for the first time since returning from injury, while former Cherry Dango Ouattara started on the bench for Brentford.
_(Image: Richard Crease)_ The first effort on goal went the way of Kroupi inside the opening two minutes as he drove at the Brentford defence and got a shot off, Hakon Valdimarsson saving well down to his right.
The next chance didn’t come until the 20th minute, and went the way of the visitors.
It was a let off for the Cherries as they gave the ball away deep in their half to Carvalho, the Bees man drove towards the Bournemouth box and put his shot just wide of the upright.
Moments later the Cherries struck the post, as Julio Soler let fly and his powerful shot got a big deflection and curled onto the base of the post, with Kluivert not far away from the decisive final touch.
Brentford took the lead after 34 minutes. Rico Henry picked out Kristoffer Ajer with a diagonal, the defender headed the ball across goal from the edge of the box and Carvalho was there to finish past Petrovic.
_(Image: Richard Crease)_ Valdimarson had to be alert to turn a cross from Christie away that came all the way through, before Soler dragged a shot well wide of the post as the Cherries trailed at the break.
Iraola went to his bench at the break and brought Antoine Semenyo and Marcos Senesi on for Gannon-Doak and Bafode Diakite.
Adli drew a save out of Valdimarsson seven minutes into the second half after he cut in from the right, before James Hill missed the target with a header from a Christie free kick.
Ouattara made his return to Bournemouth just before the hour mark, before Valdimarsson was at full stretch to palm the ball over the bar as Nathan Collins diverted an Alex Scott cross goalwards.
Brentford doubled their lead with 25 minutes left to play.
Scott was dispossessed on halfway by Frank Onyeka and he drove into the space in the Cherries half, exchanging passes with Carvalho, the ball coming to Igor Thiago with time to pick his spot past Djordje Petrovic.
Evanilson and David Brooks replaced Kroupi and Kluivert, and the Brazilian went very close to getting the Cherries back in the game.
_(Image: Richard Crease)_ He won the ball just inside the Brentford half and raced forward, playing it to Brooks on the right, who slipped him in behind and he beat the keeper with his shot but it did not have enough power on it to find the net and was cleared off the line.
Tyler Adams replaced Christie, before Collins headed wide from a Ouattara cross.
Evanilson was again denied what would have been his first goal of the season, as he did well to dispossess Collins and get a shot away across Valdimarsson from the angle, but the Icelandic stopper got down to save.
Brooks drew a comfortable save out of Valdimarsson, before Julian Araujo was sent off for a second bookable offence as the game entered stoppage time.
The Cherries weren’t able to conjure a stoppage-time comeback and they were knocked out of the League Cup.
**AFC Bournemouth:** 1, D. Petrovic; 20, J. Soler; 18, B. Diakite (Senesi 46’); 23, J. Hill; 2, J. Araujo (booked, 70’, sent off 90+1); 10, R. Christie (c)(Adams 74’); 8, A. Scott; 17, A. Adli (booked, 51’); 19, J. Kluivert (Brooks 66’); 11, B. Gannon-Doak (Semenyo 46’); 22, J. Kroupi (Evanilson 66’).
**Brentford:** 12, H. Valdimarsson; 4, S. van den Berg; 5, E. Pinnock (Thiago 59’ (booked, 80’)); 20, K. Ajer; 3, R. Henry; 15, F. Onyeka (Yarmoliuk 86’); 8, M. Jensen (c); 2, A. Hickey (Ouattara 59’); 17, A. Milambo (Kayode 59’ (booked 87’)); 7, K. Schade (Collins 59’); 14, Fábio Carvalho (booked 70’).