Warner, 26, was suspended until the first Ashes Test on 10 July and fined £7,000 (AU $11,500) after the incident early on Sunday morning.
"I struck Joe Root in the face and I'm here to apologise to Joe and own up to it," Warner told a media conference.
Jim MaxwellAustralian Broadcasting Corporation commentator
A kid from the back blocks with a strong personality, Warner is outgoing, likes talking to people and always has an opinion. He is popular with his team-mates and respected in the dressing room. He has that lively and nocturnal side to his personality. But he is 26 now, and off the field he needs to change.
He could have been sent home from the tour after pleading guilty to a charge of "unbecoming behaviour".
Australia captain Michael Clarke admitted Warner's behaviour was unacceptable.
Famous sporting confessions
"Although the punishment for David is quite harsh that's the reality when you play for the Australian cricket team," said Clarke.
"This is not an IPL team, this is not state cricket, it's not county cricket. When you play for Australia there are standards you have to uphold. His actions have not met the standard required of an Australian cricketer."
Warner's suspension means he will miss valuable match-practice as he aims to end a poor run of form.
He has made seven single-figure scores in his last nine innings while playing for Delhi Daredevils in the Indian Premier League and one-day internationals for Australia.
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