The playmaker, on loan from Real Madrid, missed over two months with a hamstring injury and has been on the bench of late but not yet played under Arteta, who took over in December after leaving his job as Manchester City's assistant head coach.
"Mikel will be a brilliant coach. He has learned from Pep (Guardiola, Manchester City coach), he has a philosophy of play which I think I fit perfectly. It's true he arrived in a difficult situation of the club, but mentally he's exactly the kind of coach Arsenal need right now," Ceballos told Marca newspaper.
"I've been working with him for around two weeks and now I have to show him I'm good enough to play for Arsenal. After the winter break I will be important," the 23-year-old added in the interview published on Tuesday.
Emery was sacked at the end of November after 18 months at the helm with Arsenal eighth in the Premier League, having endured a seven-game winless run, their longest since 1992.
"I feel impotent and angry at not having been able to help the coach (Emery) to help return everything he had done for me," Ceballos said.
He played in Arsenal's first 11 league matches but suffered his hamstring injury early in November and has not appeared since.
There were rumours he could leave in the January transfer window with Valencia, among others, linked in Spanish media.
"No, when you look at it coldly," said Ceballos when asked if he came close to leaving the Emirates.
"It seems like something silly but Arsenal fans had a song for me, there are only three or four players in the team who have their own song and they have been here for years.
"I feel loved here, each time I play at the Emirates or go out to warm up, the fans are always supporting me."
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