Your scarf has probably gone to the lost property department at Tokyo Station. 99 times out of 100 the conductors will have found your item (or someone will have handed it in), and it'll be waiting for you. That's even if it's really expensive - I left a pair of pricey Bose headphones on the Bullet train once, and was amazed that they were taken to the lost and found (at tokyo too).
Head to the Tokyo station lost property office between 9am-8pm. I couldn't find a map online, but it's to the north of the Yaesu side gates - you should look for 'wasuremono' or 'わすれもの’. You can also give them a call on 03-3231-1880 before you set out to make sure they have your it.
You'll have to fill in a couple of very simple forms, but I can pretty much guarantee you'll be reunited with your scarf!