Anichebe issued a strongly worded statement through his club on Thursday after Cheshire Police apologised for the incident on Wednesday in the affluent town of Knutsford, northern England.
The 20-year-old Nigerian international said the police apology did not go far enough.
"Whilst I do fully understand Cheshire Police's desire to tackle the problem of robberies on jewellery shops in the Knutsford area, I remain deeply upset and very angry about the treatment which was meted out to myself and a friend," he said.
"We were doing no more than window-shopping when we found ourselves surrounded by police officers who accused us of... 'attempted theft'.
"Sadly, even when I explained who I was and what I was doing, they continued to treat both of us as not just suspects but as criminals.
"It was not only totally ridiculous but also highly embarrassing and totally humiliating.
GRAB CRUTCHES
"Simply because we stood our ground and insisted that we had done absolutely nothing wrong, they decided to place my friend in handcuffs.
"I am currently having to use crutches to walk as I recently underwent surgery on a knee injury and -- astonishingly -- one of the officers even tried to grab the crutches in order to prevent me from 'escaping'.
"After what seemed like an eternity the police officers seemed to realise that they had made a mistake, acknowledging that I was a footballer with a Premiership club and not someone who was preparing to commit a crime.
"At the time, I asked the officers if they would have taken the action they did had I been white rather than black. Whilst I do not wish to turn this unfortunate and unnecessary incident into a race issue, I believe it is a question that does need to be asked."
Anichebe said that while he welcomed the police apology he did not feel "it constitutes the unreserved apology we were seeking and which we believe is justified under the circumstances."
An Everton spokesman had confirmed earlier Anichebe and his friend were peering in the window of a jewellers when police pounced, believing the pair were scouting the premises.
He said a row had ensued before the pair were released when officers realised their mistake.
Cheshire Police said closed circuit TV operators were monitoring jewellers in Knutsford and the surrounding area following a spate of violent robberies and had reported that Anichebe and his friend were acting suspiciously.
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