Former Manchester City striker Ellen White told the Women's Football Weekly podcast that Green had been the "heartbeat" of Chelsea behind the scenes.
"He had an impact on recruitment," she added. "They were always two or three years ahead of everyone else and that took them to another level.
"He had a huge part in building everything that Chelsea stands for, so it is really sad he's left. It will be interesting to see what happens now."
Green's departure raised questions over the increased involvement of co-sporting directors Laurence Stewart and Paul Winstanley, and their decision-making in relation to the women's team.
Bompastor signed a contract extension last week, keeping her at the club until 2030.
Asked whether she was happy with the level of autonomy she held at Chelsea, the Frenchwoman said: "I think I'm happy with where the club is going and the direction the club is going in.
"My job is to focus on what's on the pitch.
"My job right now as a manager is to make sure I make this team as successful as possible, I win games with my team and I give the players clarity to perform on the pitch. That's the only thing I can control and that's my main focus."
Bompastor insisted "the processess are still working and running", despite noticeable disappointments in recent transfer windows.
Following their 5-1 WSL defeat by Manchester City, she raised concerns over their summer recruitment, admitting she "would have liked to have been in a better place" after it.
The Blues did not make any signings in January, despite falling behind their WSL rivals, and had multiple bids for Paris St-Germain midfielder Jennifer Echegini turned down on deadline day.
Following recent concerns, a report in the Athletic, external suggested some players had not taken to Bompastor's training methods.
But she responded: "I know there is a lot of noise going on about our team outside the environment. I know we can't control any of that.
"But I know my players are with me. We are all together focusing on the next game and what is next in the season for us.
"I guarantee they have the trust and belief that we can achieve great things."
