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Root, a winner alongside women's captain Charlotte Edwards, averaged almost 95 in Test cricket under Moores, who was dismissed on 9 May.
"A lot of credit for that has to go to Peter Moores," said the 24-year-old.
"Over the past year, he has definitely got the best out of me - along with the rest of the coaching department."
Root was left out of the England team for the final Test of the Ashes whitewash in January 2014, but was recalled after Moores was appointed coach for the second time a year ago.
The Yorkshire right-hander has since amassed 1,135 Test runs.
"When I came back from Australia, I realised a lot of the time out there I was trying to work on things I wasn't too good at - and putting all my energy into that, rather than spending more time strengthening the stuff I am good at," added Root
"Peter saw that - and I simplified things as well."
Root, named player of the year for the men's side after a vote of cricket media, was last week appointed Test vice-captain by new director of cricket Andrew Strauss.
"I was delighted, so I accepted straight away," said Root. "I don't think things will change much - just a bit more responsibility on my part.
"If Alastair Cook wants to come up to me for ideas, I will make sure I have something to help him out."
As well as being named as the women's player of the year, Edwards was presented with a silver cap to mark her 200th game as England captain against New Zealand in February.
In addition to leading England to four series wins, Edwards averaged more than 75 in one-day internationals and almost 60 in Twenty20s.

The Scotland international has been part of a side to have kept six clean sheets in their last nine matches.
"Berra is the best defender in the league, for me, without a doubt," McCarthy told BBC Radio Suffolk.
"He's just outstanding, he's big and powerful and wins it in the air, he's quick, he blocks things and is good at defending corners."
Berra has impressed alongside youngster Adam Webster at the centre of Ipswich's defence this season, and McCarthy has previously said Webster will go onto play in the Premier League.
The pair played on Tuesday against Burton as Town ended a winless run of five matches and McCarthy's side travel to leaders Newcastle United on Saturday.
Former Republic of Ireland boss McCarthy said he was impressed by the signings the Magpies made following their relegation to the Championship, such as Matt Ritchie from Bournemouth and Dwight Gayle from Crystal Palace.
"They went out and got players who know the Championship, don't mind playing in the Championship, all want to be out of the Championship again and probably think they can be.
"How they dealt with it, they were good signings in the summer."

No such law exists, but Rishiraj Singh, the excise commissioner in the southern Indian state of Kerala, said such a stare could get a man jailed.
People online asked what might happen if a man blinked, and some quipped that sales of sunglasses would go up.
But some users said Mr Singh had raised a valid point about women's safety.
"A case can be filed against men who stare at women for more than 14 seconds," Mr Singh said in Kochi on Saturday.
The video of his statement has gone viral in the state, sparking humorous reactions and memes.
Some social media users have used dialogues from popular films in Malayalam, the language spoken in the state, to create memes.
Most users have posted memes on popular comedy Facebook pages like Troll Malayalam and ICU.
This meme implies that a teacher must shut his eyes every 13 seconds to avoid arrest.
"Just informed a girl that I didn't like her after meeting her for marriage. She threatened to file a case for staring at her for 14 seconds."
"Bro, what is your crime, stabbing or theft?". "Just went to see a girl for marriage, got convicted for looking at her for 14 seconds."
This meme shows how to time your gaze.
This meme, titled "poor lover", shows how you should interact with your girlfriend to avoid arrest.
Some social media users, however, have supported Mr Singh for raising an important issue of women's safety.
Reporting by BBC Monitoring's Zainul Abid
Batsman Joe Root has credited sacked coach Peter Moores with the form that resulted in him being named England's player of the year.
[NEXT_CONCEPT]
Ipswich Town's Christophe Berra is the best defender in the Championship, according to his manager Mick McCarthy.
[NEXT_CONCEPT]
Social media users have reacted with amused bewilderment after an official said it was illegal for a man to stare at a woman for more than 14 seconds.