I won't discuss plausibility of OP premises, I will just assume all powered machines are gone in a flash, I also assume purely mechanical machines are mostly unaffected.
Actually the percentage can even be lower than that of people not actively relying on machines.
Actual percentages are very difficult to determine, but a series of things need to be factored in:
- There are very few places in this world which are completely self-sufficient.
- Most of almost-self-sufficient populations are in remote locations; they are the only ones almost sure to survive.
- Several populations (e.g.: Amish) do not actively use machines, but are neither self-sufficient nor in a remote location.
- Self-sufficient communities in any accessible place are likely to be flooded by people from non-self-sufficient neighborhoods.
- Once population has trimmed-out enough almost all regions can be made self-sufficient.
- Many (if not all) of current high-yeld crops won't be feasible.
- Most of currently farmed land is not suitable as-is for reversal to "ancient" plantation style.
- Most of current farmers have no idea of how to rise their crops without "modern" devices.
- Most of the crops in this world are not usable for "normal" agriculture as seeds used do not give fertile plants, so seeding crops won't sprout (thanks, Monsanto!).
- After a sufficient number of people has died a series of second-stage problems will kick-in:
- Plague or similar disease will spread.
- Large structures (dams, bridges, skyscrapers, ...) will begin to fail due to lack of maintenance.
- Organized raider gangs will (try to) take over any self-sustaining community.
- Many communities will drop below the minimum level needed to keep knowledge running.
- Many communities will drop below level where biodiversity is enough to ensure healthy survival.
- Reboot of civilization might be difficult because lots of readily-accessible resources have been depleted. Some materials can be recycled from scavenged sources (e.g.: iron, plastic, asphalt, ...), but others have been fractionated into useless debris (e.g.: quicksilver, wolfram, ...).
- Much will depend on how fast some "monastic" knowledge-preserving communities can form.
Of course if "an alien civilization" is behind this then everything will depend on their long-term aims.
Update: Some comments pointed out purely mechanical machinery won't be affected by any EMP imaginable.
This is, of course, true.
OTOH in our world we are heavily (and even more so with every year) relying in electronic controllers to do the work previously done by simple mechanical devices. Whoever thinks we can go back is severely misguided; today's electronic controllers do much more than control machinery, they compensate for imperfection.
When controllers were rudimentary (e.g.: spark coils in cars or mechanical teletypes) all mechanics was highest precision because it had to work flawlessly on the given input, nowadays the same things are built in cheap plastic because the "smart controller" can track uneven movement, take it into account and (usually) produce a better result than the previous high precision (and expensive!) counterparts.
Trying to run a modern car engine without electronic control is a difficult exercise, very likely to result in a useless pile of busted junk.
Even the Army is (at least partially) abiding to this trend and relying more and more on "tactical coverage" impossible to get without electronics (e.g.: some tanks have no windows and rely on cameras to "see" outside).