Possible to use sRGB as mp4 colorspace?
You are currently probably using the Rec. 601 color space for SD video. Encode your source footage in the Rec. 709 color space.  It's the color space specified for HDTV and comes sRGB quite close.
If you need higher color accuracy you can use the Rec. 2020 color space which exceeds the sRGB color space by far. Though compatibility may not be given everywhere with this color space.