Former France defender Evra retired from football on Monday after a glittering career that included an eight-year spell with United.
The left-back played for United from 2006 to 2014, winning five Premier League titles and one Champions League crown among a host of honours.
But the 38-year-old, who had a short-term deal with West Ham last season, didn't always enjoy a smooth ride at Old Trafford.
Evra had told Woodward he intended to leave United when his contract expired at the end of the 2013-14 season, but after initially accepting his decision, Woodward announced he had triggered a one-year contract extension against the player's wishes.
Evra went ballistic and threatened Woodward when he spoke to him about the deal.
Two months later the defender, then 33, joined Juventus for £1.2 million.
"Before the end of that season Ed told me: 'Patrice, you're going to stay for another year because we've got an option in your contract,'" Evra told Sky Sports on Tuesday.
"But I told him I needed to leave because of family reasons. He shook my hand and said he understood. Then in May I was having dinner in Dubai on my birthday and had a text from my agent.
"He told me to go somewhere quiet and sent me a message with the statement from United saying they were pleased to renew my contract for another year. I went mad, I was really disappointed.
"I called Ed and swore on the phone, even threatened him. He said I couldn't talk to the director of football like that and that he was going to fine me.
"After that Ryan Giggs called and said I couldn't leave just because of one man, but it gave me an excuse to leave. I'd already said to my wife we were going to leave, but inside I didn't ever really feel I could. That gave me a little push."
Evra's revelation of the Woodward bust-up came on the same day he admitted his success in football was inspired by his humble childhood.
"I had nothing. We had nothing. But I was living as if I had everything," Evra wrote in the Players' Tribune.
"If I could tell you one secret about my life, this would be it. Anyone can be happy — anyone can love this game. Without this mindset, my friend, I would not be sitting here as a recently retired left back who played for France, Juventus and Manchester United.
"I would probably still be sitting outside a shop in Paris, begging for money to buy a sandwich.
"I'm not joking. When I grew up in Les Ulis, a commune in the Paris suburbs, I was living with my parents and some of my brothers and sisters. I have 24 of them.
"So we were about a dozen people in the same house. My father was providing a lot of our income through his job as an ambassador.
"That's what took our family from Senegal, where I was born, to Brussels and then to Les Ulis. But when I was 10 he divorced my mother. He took the sofa and the TV and even the chairs."