The league meeting between the sides was originally scheduled for January 28 at Carrow Road but will be put back a day to January 29 should Norwich win their third round replay with Fulham and earn a trip to Sheffield United on the weekend of January 25.
Newcastle had strongly opposed the potential fixture change due to the "major impact it on fans who have already booked match ticket, travel and accommodation".
And after the Premier League board, having heard both club's representations, granted Norwich's request to move the fixture, the Tyneside club made their disappointment clear.
A statement from Newcastle read: "At a time when the League are encouraging clubs to come up with initiatives to address reduced away supporter numbers, the disruption to Newcastle United fans further compounds a fixture selection clearly against the principles of encouraging away supporters to travel, given those making the journey from Tyneside are facing a midweek evening round-trip of 520 miles.
"Newcastle United notes that a condition of this potential fixture change was that Norwich City had to provide an undertaking for the reimbursement of any match day tickets returned by home or away supporters unable to attend the re-arranged match, as well as giving consideration to the cost of travel for away supporters."
Confirmation of the final fixture date will follow the FA Cup replay result between Norwich and Fulham on January 14.