Carroll had parked his Mercedes outside Cal's Own, occupying two parking spots, prompting owner Calvin Kitchin to leave an expletive laden not on Carroll's windscreen.
The forward has since responded, posting a picture of the note on his Instagram story with the caption: "I didn't like your pizza anyway."
The note from Kitchin read: "Listen you rich f****** c***, you have a nice car I'll give you that. Otherwise I pay £42,000-a-year for my lease.
"If you were to come into my restaurant and ask if you could use my parking to park nicely, me or my staff would probably say yes.
"Otherwise, you are a c***.
"You don't understand the meaning of money and/or courtesy. You are on a different planet to the working class. You do what you want, when you want.
"Hence why you can't just be nice and take what you want."
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Kitchin has since told ChronicleLive that he has "not once" seen Carroll inside his restaurant.
"What would be civilised is to come [inside] and ask if he could park his massive car, especially when there is plenty of on-street parking," Kitchin added.
"He took up two spaces - what if a disabled customer came? There is a parking meter down the road which barely costs anything anyway. He [Carroll] is the one who looks like an idiot."
Carroll is preparing for the new season at Newcastle and manager Steve Bruce recently claimed the forward was looking like "the Andy Carroll of old" after he scored an excellent goal in a friendly win over Crewe Alexandra.
Bruce said: "He was very, very good and scored a goal. It was the Andy Carroll of old, the goal. We know his qualities and the big thing is to stay well and to stay fit. He's worked ever so hard. Probably lockdown helped him and touch wood, he looks good."