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The four-goal trouncing was the latest in a long line of miserable away trips for the Robins after earlier thrashings at Rochdale (also 4-0) and Scunthorpe (4-1) with just one win from ten on the road this season (2-0 against Oldham.)
Swindon were under the cosh for the entirety of the first-half at Bramall Lane, where they have won only twice in their history, but they went into half-time at 0-0 before a second-half collapse that saw them concede three goals in the first 15 minutes of the second period.
Speaking to BBC Wiltshire at full-time in Sheffield, Williams said:
"I think it's the nature of the business that we work in: if you don't get make the grade, you get replaced," the 35-year-old began.
"That's the environment that we work in and if you don't step up then your days will be numbered.
"As the (January) transfer window draws ever closer I think a few players will be wondering if they're going to play (for us) in the new year."
Since the arrival of Tim Sherwood as director of football earlier on this season, Williams' role at the club, despire the insistence of chairman Lee Power and Sherwood himself to the contrary, has become a more reduced one.
Ex-Tottenham and Aston Villa manager Sherwood, who won the Premier League as a player with Blackburn, is in charge of transfers at the club now and, as well as that, his responsibility is team selection, tactics and team talks which were all Williams' job pre-Sherwood.
Williams still has belief in his men though.
"I never lose patience. It's my job, I'm a professional and my job is to never ever give up on a player and to try and help in any way I possibly can so I will work with the players day in, day out and if any new players come in I can then I will help them as well and that will be my role."
It was also revealed after the whistle that Michael Doughty, who was subbed at half-time for Jermaine Hylton, and missed a few weeks of the campaign with appendicits, is still ill.
"Michael is not well. He has been suffering fro a while and he doesn't seem to be able to get a clean bill of health and it's quite evident today that he didn't have energy and he wasn't his normal self so the change was obvious for us, really."
Ellis Iandolo, fresh from scoring his first goal for the club in the EFL Trophy defeat to Luton, now has a hamstring problem that ruled him out of the trip to Sheffield. His return date was not discussed.
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