Stevenson had blasted Williams on the social media site in response to comments Williams made about his ex-teammates laughing after losses during the franchise's final season in New Jersey.
"I Talk 2 My X Teammate 2Day And He Told Me That He Wasn't Talking About Me And They Mis-Print What He Said......" Stevenson tweeted Friday.
"So I'm A Real Dude And Want 2 Say Sorry 2 Dwill For Spazzing And A Real Dude Would Say Sorry! So Sorry Dwill
"Takes Alot 4 A Man 2 Call A Man And Tell Me The Truth!! I Respect That!!"
The injury-plagued Nets went 22-44 last season. Williams has called it the most frustrating year of his career, in large part because his teammates were joking around in the locker room after they "got their asses kicked."
"It was hard. I've never been in that position before," Williams said after the team completed its first day of training camp in early October. "So at times, I've showed frustration, but I think anybody would have. I think no matter who it is, if you were there every day and you saw what was going on in the locker room, you'd be pissed off, too, sometimes. You're getting your asses kicked and then you're in the locker room laughing about the game afterwards.
"I don't think that stuff is funny. That's what we had to deal with last year. But I don't think we're going to deal with it this year, because just talking to the guys, that's not what we're about. We're talking about not losing two games in a row. We were just trying to fight to win two games in a row last year."
Williams never specifically mentioned any of his ex-teammates by name.
Stevenson, traded to the Hawks as part of the blockbuster deal that brought shooting guard Joe Johnson to Brooklyn in the offseason, didn't appreciate Williams' comments and made it known on Twitter, though he didn't call Williams out by name.
"I hate Fake Muthaf----- That Quit On team but talk s--- in Espn Mag." Stevenson tweeted.
"If u gonna say ppl Quit say Names I Don't Quit I work hard period when u say that my name in it and I work hard I don't quit!!!"
"Say Names Put Address on It!!!!"
The Nets play the Hawks four times this season. The two teams play in Brooklyn on Jan. 18 and March 17. They play in Atlanta on Jan. 16 and March 9.
Mike Mazzeo is a regular contributor to ESPNNewYork.com.