Green, who returned to the lineup after missing five straight games because of a torn ligament in his left index finger, was ejected early in the fourth quarter after arguing a call.
The play in question came with 8:28 left in the contest, as Green thought he had taken a charge from Jazz guard Mike Conley. Green immediately got up and waved his hand in front of his face, disagreeing with the call. He was whistled for his first technical foul, then he picked up a second after continuing to argue with official Sean Wright.
"I disagreed with that call," Green explained after the game. "And I'm never going to be OK with another grown man telling me, 'Don't talk.' If you feel like you got the call wrong, or right, you don't tell me not to talk. I'm a grown man. I got my own kids. So that's what happened."
Warriors coach Steve Kerr, who picked up his own technical foul a few minutes later, agreed with Green voicing his opinion over what he felt was the wrong call but was hopeful that his forward could stay in games as the season progresses.
"I don't know what [Green] said," Kerr explained. "I thought it was a tough call. I thought it was a charge that was called a block, so it was a tough call. I don't know what he said, but we need him. One tech's fine; can't have two."
Aside from the ejection, the Warriors were just happy to have their emotional heart and soul back on the floor after missing over a week because of the injury.
"I thought Draymond looked good," Kerr said. "He was a little rusty his first run, and then after that first run, he looked much better. He's easing his way back from injury, but he's also easing his way into a team he's never really seen before.
"These circumstances are really bizarre for him, for Draymond, when you think about where we've been the last few years. And how he's played and with whom he's played. And now it's a totally different look; we're running a different offense. So he's trying to find his place in all that."
Both Kerr and Green noted just how much the offense has changed over the past couple of weeks, after guard Stephen Curry broke his left hand on Oct. 30 and the Warriors built more sets around new guard D'Angelo Russell.
"This is a completely different offense," Green said. "It's not our normal offense. Just adjust to that. Kind of find my spots and kind of find out where you fit in the offense, where I fit in the offense, and spacing, different stuff like that, which will happen pretty quickly. But more importantly, just really try and get a rhythm and my wind."
Kerr echoed similar sentiments.
"Over the last week, we've really changed the way we've played with our offensive sets and how we've attacked teams. So it's kind of a strange case where the guy who's been here the longest all of a sudden is the newest with what we're doing," Kerr said of Green. "So just to go along with everything else that's happened this season, it's another sort of bizarre twist.
"But he and I have talked about it and we're good. He's going to do everything he can to help these young guys come along, and he'll fit in with what we're trying to do, and he'll get better and we'll get better."
Green finished on Monday with four points, seven rebounds and four assists in 22 minutes.
"Just got to get a rhythm again -- and my wind," Green said. "Ten days, opened those lungs up like you do in the game, it's a little different. Obviously, I wasn't able to practice or nothing. We had [Sunday] off, and the team was gone for a week, so I haven't been able to play. I've just been working out, and that's always different; so I just got to get my wind back, but that will come back pretty fast."
Green, who was accustomed to initiating a lot of the offense in recent years while playing alongside Curry, Klay Thompson and Kevin Durant, said the change to the new system is different but that he is confident he will get used to everything in due time.
"I don't really have the ball in my hands," Green said. "I've always been a playmaker. I don't really have the ball much, so it affects, but it's nothing. It is what it is. Just figure it out. It's not the first time in my career I've had to figure something out. It takes a little time to do, but it's no big deal. It is what it is."
The Warriors' younger players are glad to have the veteran leader back on the floor, even if Green still is figuring out exactly where to be throughout the game.
"He just tries to help us see the next play," Warriors rookie forward Eric Paschall said. "So whatever if it's offensively, defensively, he knows the other team's calls. Whatever it is, if he knows the other team's calls, he's trying to say it fast, just like, 'Oh, this is what they're doing.'
"So, Draymond is just a great leader to have on the floor at all times, just because he's so smart in what he does and he's such a high-level competitor that it's always great to have that type of guy on the floor at all times."