"Any time you get a text message saying that it's happening, you feel like you got punched in the stomach," Jackson said during his weekly appearance on WGR 550 in Buffalo. "I mean, stuff could have been handled different. We don't ... we all weren't in the room and understand what went down."
Jackson, a team captain and one of the Bills' most tenured players, added that players must now "move on" after Marrone exercised an opt-out clause and terminated his contract.
Marrone reportedly sent a mass text to his players after the news of his opt-out was announced, telling them to call him if they had any questions.
"It's the unfortunate part of the business," he said. "Everybody makes decisions that best suits them. For us, we're not going to dwell on what he decided to do."
The New York Jets interviewed Marrone on Sunday, but Jackson downplayed the effect of Marrone potentially jumping to a division rival.
"No, he's just gonna be another guy," Jackson said. "Obviously, we'll want to beat him when we play him. But it's not going to fuel or motivate us in any different capacity. He's just another guy now. He's not somebody that we're worried about what he's doing."
Jackson was not alone in criticizing Marrone's surprise decision to step down.
Bob Casullo, a former NFL special teams coach who served as an assistant under Marrone at Syracuse, made an even stronger complaint Monday.
"Self-centered, selfish, greedy...He'll get a job because there aren't enough quality people with head coaching experience to get these jobs," Casullo said on ESPN Radio Syracuse. "(Arizona coordinator Todd) Bowles, (Seahawks coordinator Dan) Quinn, (Lions coordinator Teryl) Austin, (Bengals coordinator) Hue Jackson had a job and should get a job. There are about nine or 10 guys that should be getting these jobs and you're just reshuffling an egomaniac, less than .500 coach."
Marrone, who was hired after four seasons at Syracuse, went 15-17 in Buffalo.
The Bills have requested head-coaching interviews with Browns coordinator Kyle Shanahan, a source told ESPN NFL Insider Adam Schefter on Monday, and several other candidates, with owner Terry Pegula and general manager Doug Whaley involved in the search.
"[We] put all our faith in the Pegulas to get this thing fixed and get us a great coaching staff to come here," Jackson said. "Somebody that is here and wants to be here and we're excited to play for."
The Associated Press contributed to this report.