It appears that your design is focusing on creating a star-shaped outline rather than a solid star shape.
<!DOCTYPE html>
<html>
<body>
<svg width="260" height="245" xmlns="http://www.w3.org/2000/svg" fill="rgb(240, 240, 240)" stroke="transparent" stroke-width="1">
<filter id="inset-shadow" x="-50%" y="-50%" width="200%" height="200%">
<feComponentTransfer in=SourceAlpha>
<feFuncA type="table" tableValues="1 0" />
</feComponentTransfer>
<feGaussianBlur stdDeviation="1"/>
<feOffset dx="0" dy="2" result="offsetblur"/>
<feFlood flood-color="rgb(20, 0, 0)" result="color"/>
<feComposite in2="offsetblur" operator="in"/>
<feComposite in2="SourceAlpha" operator="in" />
<feMerge>
<feMergeNode in="SourceGraphic" />
<feMergeNode />
</feMerge>
</filter>
<path filter="url(#inset-shadow)" d="M12 .587l3.668 7.568 8.332 1.151-6.064 5.828 1.48 8.279-7.416-3.967-7.417 3.967 1.481-8.279-6.064-5.828 8.332-1.151z"/>
</svg>
</body>
</html>
Paulie_D shared some valuable resources which were used and slightly modified to bring you closer to the desired image example.
Edit: The user mentioned a preference for a transparent fill in the comments. Source. This method differs from Sviat Kuzhelev's answer as it involves using one continuous path for the shape instead of creating separate disjointed lines.
<html>
<body>
<svg>
<defs>
<filter id="inset-shadow" width="200%" height="200%">
<!-- Shadow Offset -->
<feOffset dx="0" dy="1" />
<!-- Shadow Blur -->
<feGaussianBlur stdDeviation="1" result="offset-blur" />
<!-- Invert the drop shadow to create an inner shadow -->
<feComposite operator="out" in="SourceGraphic" result="inverse" />
<!-- Color & Opacity -->
<feFlood flood-color="black" flood-opacity=".75" result="color" />
<!-- Clip color inside shadow -->
<feComposite operator="in" in="color" in2="inverse" result="shadow" />
<!-- Shadow Opacity -->
<feComponentTransfer in="shadow" result="shadow">
<feFuncA type="linear" slope="1" />
</feComponentTransfer>
<!-- Put shadow over original object -->
<!--<feComposite operator="over" in="shadow" in2="SourceGraphic"/>-->
</filter>
</defs>
<path filter="url(#inset-shadow)" d="M12 .587l3.668 7.568 8.332 1.151-6.064 5.828 1.48 8.279-7.416-3.967-7.417 3.967 1.481-8.279-6.064-5.828 8.332-1.151z" />
</svg>
</body>
</html>