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Ceballos, who is currently on loan to the North London club, previously said he had not been happy in La Liga.
Addressing those quotes in an interview with Spain's Radio Marca while on international duty, Ceballos said: "My words were misunderstood."
He said: "A player is not happy if he doesn't play, but when he feels important and does play, then he is happy.
"Obviously I have been at Real Madrid, I have learnt from the best and I have won trophies, but it is easier when you play.
"I'm happy and I feel important [at Arsenal], with room for improvement to play at the Euros next year."
However, the 23-year-old clarified: "When I do not play, I don't enjoy myself."
In what will no doubt be a blow to Arsenal manager Unai Emery, the Spain international confirmed his desire to ultimately return to Madrid.
He said: "I never thought of leaving permanently - my goal is to succeed at Real Madrid. I'm going to fight to fulfil my dream."
Sir Bradley Wiggins & Lizzie Deignan