Upvote:2
According to this independent oyster guide, in case of a top-up by payment card (credit or debit) if the second tap fails then the payment will be authorised but it won't be debited, and you should see the payment authorisation disappear from your card statement in the following days:
If you pay by card then the transaction will be authorised after you enter your PIN. If you forget to touch again to get the top-up added then this authorisation will remain and may appear as if the money has been taken. It hasn’t, and the authorisation will drop off 2-3 business days later when TfL will have failed to charge the debit to your bank.
Since you forgot to re-tap after topping up by cash I am afraid there's not much you can do to claim a refund. Moreover I assume you don't have a receipt either, since these, along with change, are released after the second tap. Your best bet would probably be to contact the Oyster helpline at 0343 222 1234
or using the online enquiry form and ask, or to ask someone at a a manned ticket office in any station.