Bournemouth fell to a 3-2 defeat, despite leading 1-0 at the break thanks to a Daniel Adu-Adjei goal and drawing themselves level at 2-2 through Harold William.
But a goal ten minutes from time handed the Bees the victory at the Vitality Stadium.
Reflecting on the game, Kinsey said: “We're all devastated, to be honest, as you'd expect.
“We knew Brentford would come here, they're a strong side, I said this after the Burnley game. I think they’ve spent quite a lot of money, they brought some quality players here today.
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“But I think we have a real quality group as well. And I think we put on a real performance here tonight. I think we show the fans what we can do.
“It was unfortunate that the result obviously went the way it did, but that's football and we’ve got to bounce back.
“But I feel like to do what we've done the past two, three months in particular has been incredible. And I'm really proud of the boys.”
Kinsey said the side came into the dressing room feeling positive at 1-0 up, but they were aware that the game could change quickly.
“We were stressing that, the fact obviously that it can change like it did going 2-1 down,” he said.
“But even to bounce back from that against the good side, get a little bit of luck in there, maybe a ricochet.
“But to finish it off and then to push until the end, I feel like we all physically and mentally pushed, stuck together, but just unfortunately fell the wrong side of the result.”
Brentford’s second and third goals were brilliant strikes, Romelle Donovan striking into the top corner from 25 yards and Tony Yogane curling home at the far post from just outside the box.
And Kinsey admitted Brentford showed their quality.
“But I feel like likewise with us, we have some real quality players and we did show it tonight, but two of them were worldies,” he said.
“I think the last one even was a little bit of a deflection as well, which hurts even more. But that’s football sometimes.”