Press your lips together, add vocal cord vibration, then release.

Americans pronounce brought as BRAHT (/brɔt/). You'll hear it in sentences like "Bob brought a bunch of balloons for the baby" or "The k-9 unit was brought in to search for drugs" — more examples below.
Record yourself saying "brought" and play it back. The mic stays on your device — nothing's uploaded.
1 syllable, 4 sounds. Explore each sound's mouth shape and how it's made.
Press your lips together, add vocal cord vibration, then release.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
Relax your lips and drop your jaw significantly. The tongue tip lightly touches behind the bottom front teeth and the back part of the tongue presses down a little to create more dark space in the back of the mouth.

Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

Click any sentence to see the full breakdown — every link, every reduction, every flap-T.
The textbook way isn't wrong — it's just not how anyone actually says it.
In "brought", the "t" is not released — the articulators get into position but hold without the burst of air. Air stops but there's no release burst — the articulators hold position.