I'm going to be contrary and say yes.
I don't know how your dragons entered this world or how your actual apocalypse event sequence plays out. I'm giving a solution that I think can help out in many scenarios with a little tweaking here and there.
tl/dr I believe you will have to create an apocolyptic scenario that destroys infrastructure and the ability to rebuild and creates an environment where knowledge is lost, rapidly!
When the dragons first arrive on the scene they find a world rich in electricity and iron based infrastructure. Iron just so happens to increase their fertility/breeding capabilities. Soon your world is overrun by large numbers of dragons, mostly juveniles.
Iron does something to the dragon physiology and increases the ability to lay eggs. Lots of eggs. All over the place. Dragons crave the iron and scavenge it from everywhere they can find. They demolish alot of infrastructure creating their nests/creating iron hoards/ etc.
Juvenile dragons have a really bad habit of burping electromagnetic pulses (EMPs). This could be coupled with larger electromagnetic pulses being released when the dragon eggs break. (However you want, just make sure to destroy the ability to communicate over distance and share electrical knowledge.)
This fries all nearby electric circuitry. You can have these pulses what ever size you want but as there are a lot of eggs laying around in the cities and highly developed parts of the countries around the world, these areas soon loose all electrical power and most of their infrastructure.
- So what, that doesn't stop people from learning!
Well, most of the knowledge is now locked up on the dead internet and fried computer circuitry. Actual physical libraries (those that remain, there has been a general trend of closing book libraries the last few years) are nearly always going to have some sort of electrical and iron components in them ie temperature control systems/shelving/overhead lighting/ stools. The dragons destroyed the buildings when they went after the iron and steel in the walls and possibly even burnt all the books at the same time.
- But you don't want a "current day" story world so overrun with dragons?
Once the easily located iron has been found and used up, the dragons fertility/egg laying spree decreases to a more natural balance. This allows for lower dragon numbers over time.
The large mass of juvenile dragons can be very territorial/agitated/what ever your story has already deemed. Too many juveniles in the same area could result in fights to the death. Lots of buildings demolished, lots of fields and forests ravaged, lots of electromagnetic pulses released etc. Eventually the dragon numbers diminish and the dragons reach a more harmonous balance with each other/environment.
- but I need some electrical artefacts to survive!
You can make the dragon's iron/metal sensing capabilities be as sensitive as you require. Maybe they can't sense lone items unless they are right on top of them. Maybe they are sensing the accumulated iron artefacts. So a single item or two that is well hidden could survive. This will allow your survives to keep their steel and metal knifes/carabiners/belt buckles/retainers/fillings/hip replacements etc.
Coupled with later dimished dragon numbers this also allows for some very well hidden artefacts (faraday cage protected) and forgotten artifacts to survive without the constant threat of a juvenile dragon or exploding egg to release an electromagnetic pulse in your current story world. While at the same time preventing major rebuilding of electrical infrastructure in the past.
- what about the people hoarding books and equipment?
Well, when the military and doomsday survivors first started building their concrete bunkers with lots of steel reinforcements they weren't planning on the dragon apocalypse. After the first few electromagnetic pulses went off in the cities across the world, they went to their standard plan book. They retreated to their bunkers. They also in their wisdom gathered up all the smartest people they could find and tried to save as many books and artifacts that they thought would be useful. When the dragons came...everything went up in smoke. There goes the military and all the smartest people...and the people mostly well prepared to survive.
- So where did people hide to survive?
Those that managed to get out of the cities and developed town areas, scattered into family units and occasionally coalesced into some gang like tribes (standard post apocalypse setting). Only/mostly those that avoided relying on iron survived. Most that survived ended up holing up in natural cave systems. Just barely surviving. Eeking a subsistence farming lifestyle if lucky. Hunter/gather style mostly.
- Many of these groups know how to read and write. Why would that be lost?
Why not. Story based logic can explain why survival groups wouldn't have the time or resources to waste on an old-world skill. Besides, not alot of survives grabbed any books when they ran for it. Most of them grabbed their smartphones and chargers. Nice pretty paperweights now.
You can use any logic you find explainable how they lost/regained the ability to read. It probably won't be lost immediately, more like a few generations. But it will definitely be a skill most likely to be put aside by the more "macho, I'm too busy hunting for your food to take the time to learn to read...well". The ability to mine and extract, and even work, new iron would probably have to be refound altogether. Blacksmiths are a dying breed today and most who know how to extract iron probably died in the mines and extraction plants that the dragons tore apart.
After that, it's up to your story how they regain their knowledge. Find a few books that they can no longer read here and there. By then their language has probably shifted into a polygot of any languages that made up their original survivor groups. Each group having a unique language/dialect etc. With a few iron artefacts that survived the iron craze of the early dragon arrival. Etc.
So iron/metal sensitive dragons. Some sort of increased fertility that decreases after an initial explosion in drsgon population numbers. An iron craze leading to destruction of physical infrastructure (and physical libraries) and a loss of easily reusable iron in later years. Electromagnetic pulses of some origin, destroying communications and digital libraries. Continued electromagnetic pulses preventing rebuilding of technology while knowledge is still known. Mass casualties of untold numbers. Post apocalypse survival scenarios of your choice.