The 27-year-old United captain was given a suspended sentence of 21 months and 10 days after being found guilty of repeated bodily harm, attempted bribery, violence against public employees and insult after his arrest on Mykonos.
However, Maguire told BBC Sport plain-clothed police officers, who he says did not identify themselves, pulled over his group’s minibus, threw him off the vehicle and hit him in his legs.
Maguire said he tried to run away because he had no idea who the men were.
“They hit me a lot on the legs. It wasn’t on my mind. I was in that much of a panic. Fear. Scared for my life,” he said.
The central defender said his “conscience is clear”.
He denied throwing any punches or trying to bribe the police.
“I don’t wish it on anybody. Obviously the situation has made it difficult for one of the biggest clubs in the world, so I regret putting the fans and the club through this, but I did nothing wrong,” he added.
“I found myself in a situation where it could have happened to anybody and anywhere.”
On Wednesday, Maguire’s legal team lodged an appeal against the verdict.
Under Greek law, the appeal nullifies the original conviction so there will be a full retrial.
Maguire’s brother Joe and friend Christopher Sharman were also found guilty on a range of charges and sentenced to 13 months in prison, suspended for three years.
The three men denied all the charges.
According to media reports, a fight started at a nightclub over claims Maguire’s sister Daisy had been injected with what the defence said was a suspected drug.
England manager Gareth Southgate withdrew Maguire from his squad for the Nations League matches against Iceland and Denmark next month, having initially selected him on Tuesday.