I have flown Turkish Airlines Istanbul-Kuala Lumpur and Singapore-Istanbul.
I asked for Miles & More mileage and the Singapore-Istanbul flight is excluded from mileage awards, since I have booked in Economy class Y. Couldn't find any proof of that on the website.
Are Miles & More award miles due for Y class travel?
Depending on the airline, not all flight are eligible for earning miles. Sometimes very discounted fares will earn either a reduced number of miles, or possibly none at all.
The Miles & More website has a page for each of their partner airlines that lists which fare classes are eligible for earning miles, and at what rate.
According to their page for Turkish Airlines :
It is not possible to earn miles in booking classes G, P, W, Z (and worldwide V).
All other fares appear to earn somewhere between 0.5 and 2.0 times the number of miles flown, so I presume that you were on one of the fares listed above.
Note that "Y" frequently refers to two different things - it is normally a fare code for a full priced economy ticket, but it's also often used to refer to any economy ticket. Thus whilst you do have an "Economy Class" ticket, you likely don't have a "Y" class ticket.
You may still be able to get credit for those flights on a different airline. eg, sometimes even if Miles & More doesn't allow credit, either the operating carrier themselves (ie, Turkish) or another partner airline like United might allow collection of miles for those fare classes - just be sure to check their first!
miles-and-more.com has an online form "Mileage request" to add a flight to your mileage account, if this hasn't happened automatically.
I would just try to add the flight with this form, if that's not possible probably your used booking class is excluded from earning miles.
