Debit cards can't be used for online payment/phone payment etc, unless said balance is deposited via the bank account connected to the Debit card via PayPal, MB, etc.
It's not the fact that people don't accept debit cards, it's the issue that you can't actually pay with a debit card on its own, as you can with a credit card (online). You can however bank transfer, which is essentially paying via your debit card.