Usual tickets vending machines of JR East doesn’t accept any credit cards except for View Card. View Card is issued by JR East Group. It is very inconvenient for foreign travelers.
I get how to buy a ticket with other credit card. I heard it from a officer of JR East.
You will be able to find a special vending machine at stations. This type machine can handle standard credit cards. This machine is a only solution to buy tickets with non View Card. Of course, you can buy a ticket at ticket counter that is “みどりの窓口".
Unfortunately, this type machine might not be found small scale stations.
You can touch the red rectangle on its display. It is a buying button for a short distance ticket.
Select ticket’s fee and insert your credit card, then type pass code. You will get a ticket.
“C制" mark is a evidence for buying with a credit card.
(Added at 2015-04-07 00:02)
The following page is describing how to buy a ticket. However, you cannot get how to buy a ticket with your credit card on a vending machine. It is terrible.