Paul Dickov retained his job as Latics manager ahead of this week's 2-2 draw at Scunthorpe despite assistant Gerry Taggart, reserve-team boss Lee Duxbury and fitness coach Paul Butler being removed by the npower League One club's board.
Furman said: "We're the ones who are out there every week. The staff do all that they can for us during the week and on a matchday before three o'clock.
"It's us whose out there at three o'clock and a poor run of form from us on the pitch has coincided with them losing their jobs.
"So we're 100 per cent feeling some part responsible for the loss of their jobs and we have to hold our hands up to that."
Furman admitted the players had to put feelings of sadness to one side before the trip to Glanford Park and he is ready to do the same ahead of this weekend's FA Cup clash with Nottingham Forest.
"It's tough," he added. "Personally I've been here for a long time now and I've worked with the three staff who've lost their jobs for the last three or four years.
"In a football club you sometimes see people here more than you see your family so you become very close to people. So to see people lose their jobs - it's very sad.
"But that's football. We've spoken to them, we'll stay in touch and we wish them well but we had a job to do on Tuesday and we couldn't dwell too much on what had happened.
"Sadly that's the way football goes and sackings do happen. We are very sorry for the loss but we have to get on with the rest of our season now."
- Sports & Recreation
- Lee Duxbury
- Gerry Taggart
- Paul Dickov