Josh Dasilva's second-half strike was enough to seal The Bees a place in the last four of the competition, a goal that mounts even more pressure on Magpies head coach Steve Bruce.
Here are the most important responses Newcastle boss made to the media in his post-match press conference this evening:
A disappointing and frustrating night
When asked for his immediate reaction to the game, Bruce said he was 'bitterly disappointed' with how it went and said that his side struggled to create many clear-cut chances throughout.
"Bitterly disappointed and very, very frustrated tonight.
"You genuinely believe you could score but we had one or two instances where it didn't quite fall for us.
"But we didn't really create much at all.
"Jacob [Murphy] had a moment where he overran it in the first half but in the end you need to have a bit of a break and it didn't go our way."
The game was always going to be tough
Bruce believed that the game would be a difficult task, but 'expected' a good showing from his players.
"We're all desperately disappointed of course because of the opportunity we had.
"I always knew it would be difficult but I still expected us to perform better than what we did."
No time to dwell on defeat
The Magpies head coach said that his side have no time to lick their wounds, as they must immediately prepare for the mammoth task that is Manchester City on Saturday.
"We haven't done enough.
"We have to accept what's coming our way and dust ourselves down for what is a huge challenge ahead of us in the Premier League.
"They come thick and fast, but I can't hide my disappointment because we have a great opportunity today to get into a semi-final."
Strong cup sides will continue
The Toon boss said that he will continue to play strong sides in the cup, then went on to praise Brentford for their impressive performance.
"I stand by what I said when I walked through the door and that's that I'll treat the cups as I see fit.
“I picked a team I thought was good enough to win the match.
“Unfortunately Brentford played very, very well on the night and caused us problems but I'm disappointed we didn't perform better than we did."
On his future as Newcastle boss
After tonight's bitter defeat to a side in the division below, fans have become more and more frustrated with Bruce, with a large section of supporters calling for him to be sacked.
Bruce says that the criticism is 'fully justified' from the fans, and acknowledges that his team were not good enough tonight.
"I’m a resilient so-and-so so I’ll need to be ready for what’s coming my way.
"The supporters are entitled to their opinion and I accept that.
"I can't let that affect myself.
"I accept what's coming my way.
"The criticism is fully justified.
"We simply haven't played well enough to win."