Press your lips together to stop the air, then release. No vocal cord vibration.

Americans pronounce postponed as pohst-POHND (/poʊstˈpoʊnd/). In "postponed", the "t" is squeezed between other consonants and drops out — the surrounding consonants flow together without it — most natural in flowing, casual speech; in careful or formal speech, the T may be lightly present. This is called the Silent T in Clusters, a small move that separates 'classroom' from 'native'. It comes out as pohst·POHND. Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "The rain delay caused the match to be postponed" or "The event has been postponed until further notice unfortunately" — more examples below.
Record yourself saying "postponed" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 8 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Press your lips together to stop the air, then release. No vocal cord vibration.

Start with your mouth slightly open, then close your jaw slightly as your lips round. Shift your tongue back slightly, then stretch the back up.
Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

The T is skipped entirely. Your tongue doesn't make contact at the T position.

Press your lips together to stop the air, then release. No vocal cord vibration.

Start with your mouth slightly open, then close your jaw slightly as your lips round. Shift your tongue back slightly, then stretch the back up.
Touch the tip or front edge of your tongue to the roof of your mouth behind your teeth. Air flows through your nose.

Touch the tip of your tongue to the roof of your mouth just behind your teeth. Add vocal cord vibration as you release.

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 "postponed", the "t" is squeezed between other consonants and drops out — the surrounding consonants flow together without it — most natural in flowing, casual speech; in careful or formal speech, the T may be lightly present. /t/ is dropped entirely — the surrounding consonants flow together without the T.
In "postponed", the "d" 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.
Stress falls on the second syllable, not the others. Stretch POHND — keep everything else short and quick.