Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

Americans pronounce systematic as sih-stuh-MA-tuhk (/ˌsɪstəˈmæɾək/). In "systematic", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. This is called the Flap T, and it's why Americans sound more relaxed than the textbook. It comes out as SIH·stuh·MA·tuhk. Stress falls on the third syllable — keep everything else short and quick. You'll hear it in sentences like "He organized his study materials in a systematic way".
Record yourself saying "systematic" and play it back. The mic stays on your device — nothing's uploaded.
4 syllables, 10 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

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.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
The schwa before M disappears — M becomes the vowel of the syllable. Go straight from the previous consonant to M.

Drop the jaw noticeably. Keep the body of the tongue low and forward, and don't let the back of the tongue raise toward the soft palate. Pull the lip corners back slightly, almost a starting smile.

Quickly bounce the front of your tongue against the roof of your mouth. Don't stop the airflow — just a quick tap.

Relax your lips, jaw, and tongue completely. Drop your jaw slightly and keep the tongue neutral.
Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

The textbook way isn't wrong — it's just not how anyone actually says it.
In "systematic", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. /t/ or /d/ becomes a quick tap [ɾ] — sounds like a soft D. The tongue briefly taps the ridge behind the upper teeth.
In "systematic", the "k" 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 third syllable, not the others. Stretch MA — keep everything else short and quick.
Don't pronounce the first syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.