But Paxson insists the front office has a "really good" relationship with its coach.
"Look, it's not realistic to ask Tom or his staff to be happy about taking a player of Lu's caliber off your team," Paxson said Tuesday. "[General manager] Gar [Forman] and I put ourselves in Tom's shoes a lot. Every day, really. And we know what he's facing. We're not sitting up here saying be happy about it. It's hard. It's difficult.
"But what has to happen within an organization is that when decisions are made, that as a group you have to align together, and you have to move forward. And our focus now has to be on how best to take advantage of what we've just done. That's the challenge -- and Tom's going to be a part of that process with us. That's how this works."
The Bulls traded Deng, their All-Star forward who will be a free agent at the end of the season, to the Cleveland Cavaliers for Bynum, draft picks and salary savings early Tuesday morning.
As expected, the Bulls waived Bynum on Tuesday afternoon, clearing his $12.3 million salary off their books. That will enable the Bulls to get below the luxury-tax threshold, which, combined with not having to pay Deng the balance of his $14.3 million salary, will save the team more than $20 million.
Bynum is expected to clear waivers and become a free agent by the end of the week. Though he was suspended by the Cavs for one game for conduct detrimental to the team and excused from team activities, he is expected to be chased on the open market. The Los Angeles Clippers, Miami Heat and New York Knicks are among the teams expected to consider offering him a landing spot.
Expected to contend for the East title at the beginning of the season, the Bulls are looking to the future after losing Derrick Rose in November to another season-ending knee injury and now trading their two-time All-Star forward.
"I had a chance to voice my opinion," Thibodeau said of his meeting with the front office before the trade was made. "Their job is to make financial decisions, to make player personnel decisions, and things of that nature. Their job is to do that. My job is to coach the guys that are here. That's the way it works."
Asked if he disagreed with the trade when he talked about it with the front office, Thibodeau said, "We discussed it, and I'll leave it at that."
It's uncertain how Rose, who was consulted by the Bulls about the trade and spoke at length with chairman Jerry Reinsdorf on Monday night, feels about the deal.
Thibodeau said the Deng deal, and the events surrounding the Bulls' decision to rebuild their roster, would not impact his relationship with Paxson or Forman, which was reportedly strained over the summer when the team decided not to retain Thibodeau's lead assistant, Ron Adams.
"No, because you want to communicate with everybody," he said. "Your owner, management, and sometimes things may not go your way, but you have to be professional about it. You have to move forward. There's a lot of decisions that get made. And as long as you have your input, that's all you can ask for. Everyone has to do their job. My job is to coach the guys that are here, and that's all I'm thinking about."
Paxson knows he just made Thibodeau's job more difficult by trading Deng.
"We respect Tom a lot," Paxson said. "And speaking to him this morning, he's the head coach of the Chicago Bulls. He wants to win the games. We all want to win the games. And this makes it more challenging, and we know that. But we have great faith in his ability and we also have great faith in the fact that this gives us the best opportunity going forward to create a deeper roster. One that will give us a better chance to win going forward."
Thibodeau said he shared a personal message with Deng, whom the coach has called "the glue" of the Bulls, after the deal went down.
"I thanked him for all that stuff that he did," Thibodeau said. "It's almost 10 years. I think he was a big part of lifting the team out of the five or six years in the lottery before he got here. Then what he did for me. You couldn't ask anything more of a player. Practice hard, be a great leader, play for the team, be selfless. Whatever I asked him to do, he did. And he bought in from day one, from the minute I got here.
"So I appreciated that and I thought when you look at what he did, the way he worked and the way he performed, those are two things I value greatly. And then when you add to it the type of person he is, all the things that he did in the community. He embodied what we stand for. Lu was never the type of guy that would call attention to himself by the things that he did. He did a lot of good things in this community because he felt it was the right thing to do."
Deng offered a goodbye to Chicago via Twitter.
"You will hear a lot of can't and a lot of won't, but you give it everything you can because you believe in yourself and your teammates. You push yourself with your heart, mind and soul, and smile every night knowing you put love and passion into it. Thank you, Chicago," Deng wrote.
The Bulls got a future first-round draft pick owed to the Cavs by the Sacramento Kings from a 2011 trade for J.J. Hickson. The Bulls will get the Kings' pick if it falls outside the top 12 in 2014 or outside the top 10 picks in 2015, '16 or '17. The Bulls also got the 2015 and '16 second-round picks the Portland Trail Blazers owed the Cavs. In a final piece, the Bulls will be able to swap draft positions with the Cavs in 2015 as long as Cleveland's draft pick is outside the top 14 picks.
In addition to their own draft pick, the Bulls also own the Charlotte Bobcats' 2014 first-round pick if it falls outside the top 10. They also own the rights to star Spanish forward Nikola Mirotic, who they hope to bring over to play next season.
Paxson also said Tuesday a decision on whether to amnesty the final year of Carlos Boozer's contract has not been made yet.
"Everybody knows that we have the amnesty clause available to us. And it's a decision that will be made but it's not being made today," Paxson said. "It will be made at some point, but you can't do it now if you want to do it. But let me say this about Carlos, OK, because I think Carlos sometimes gets a little bit unfair criticism. When you think about the last three or four years, the one player who has practiced every day, played almost every game, come into the practice facility or the United Center with a positive attitude has been Carlos Boozer.
"He's been good for our team, he's been good for our guys. And we take those things into consideration. No decision has been made and the fact is we don't have to make that decision today so it's not worth discussing really."
ESPNChicago.com's Nick Friedell contributed to this report.