Although Blender cannot export as MP4, you can render an image sequence into video format and then convert it to MP4 using Blender or third-party software.
How To Export Blender Animation (MP4)
Export Slate Animation as Series of Images: In the Output Properties tab, you can choose a folder where you want to save rendered frames.
To save a series of images, set the output file format to PNG or JPEG This is the best way because it adds more legroom in post-processing.
Render the Animation: After setting the settings, hit F12 to start rendering your animation as an image sequence. This will save each frame of the blender as a different file.
Convert to MP4: When the image sequence has been rendered, go to Video Sequencer (in Blender).
Import sequence, change File Type to FFmpeg Video and MP4 for Encoding.
Choose the option MP4 as your container, and pick a video codec (H.264 generally is what you want).
Click File→Render Animation to export the image sequence into an MP4 file.
It exports in high quality as well with adjustments that can be made during post-production.
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