Not having been directly stabbed this is a bit removed, but every time I've been in a high-adrenaline situation and blood has been drawn, I didn't notice right away. Usually I was going about my business afterwards and someone screamed because I was bleeding a lot and didn't notice.

Also from a filmmaking perspective - it's not always about what's correct so much as what makes for a good movie. In a high-octane action scene someone might scream as they get their head sliced of despite that being physically impossible, but it makes for good cinema in some peoples' eyes.