I cannot speak about all ancient peoples but I can use examples from the Chinese and the Greeks for whom we have documents. Both considered the Earth to be the center of the Universe. Being the center all material seemed to fall to it. If one rode on a cart one felt motion. Since there was no perceptable motion when you stood on the ground it was assumed not to move. The fact that the heavens moved was not thought of as evidence that the Earth moved but of their own motion. The Chinese though that stars were suspended from a ceiling or the underside of an umbrella. The Greeks thought that the stars were fixed to a giant hollow sphere that was all around us.
The only record that we have of someone who thought the Earth moved was Aristarchus of Samos, who thought that the Sun was the center of the Universe and not the Earth. Unfortunately we don't have information on what he thought of the Earth's motion and why we don't perceive it.
When Copernicus presented his model of the Sun centered universe the fact that we don't erceive motion was a big objection. It took almost 150 years for Galileo and Newton to undertsand and explain why we don't perceive the motion and why we don't fly off the Earth if it is moving.
Ancient Greeks and other peoples believed the earth to be the still centre of a rotating universe. As one stood on the earth's surface there was no perceptible movement, whereas people saw the sun rise in the east every morning and set in the west every evening. They also saw the stars and planets appearing to move across the sky. By the 4th century B.C. the Greeks had developed a picture of the stars as fixed on a celestial sphere that moved around the earth, with the Sun, the Moon, and the planets moving independently beneath it.
This model of geocentric universe, known as Ptolemy's model, came to be challenged from the 16th century by astronomers like Copernicus, Tycho Brahe and Galileo, which has led to the present model of heliocentric universe.