The Scotland international, 26, has spent a lengthy spell on the sidelines with an ankle injury but with Fulop due to be rested, he can reassert his claims for a recall when he returns to front-line duties in Wednesday night's FA Cup fourth-round replay at Blackburn.
"Craig's a bit worried about what is happening in general but I told him to carry on where you are going and we will start you on Wednesday and hopefully get 90 minutes," Sbragia said.
"Marton has done extremely well and is keeping others out and long may it continue. Craig knows he has a fight on his hands now.
"Before he probably thought he would walk in automatically but we need competition in every area on the field and that has come out of the blue with Marton coming in and doing so well.
"Nobody's place is guaranteed. We just see how far down the line he is. He's probably played two games in 12 weeks."
Sbragia also revealed a "cheeky" bid – believed to be worth £6million – from arch-rivals Newcastle for former Manchester United midfielder Kieran Richardson had been rebuffed.
"There was an inquiry and we rejected that right away," Sbragia said.
"He's an important member of the team. They came in with a fee. Even if it'd been a high one I wouldn't have accepted it because I want to keep him. It wouldn't have been ideal to sell him to Newcastle."
He also revealed Tottenham striker Darren Bent was on Sunderland's radar.
"We were interested in him, but we weren't certain whether he was going to become available," Sbragia added. "Niall Quinn [Sunderland chairman] was involved in that one far more than I was.
"But I think maybe the Robbie Keane deal came through too late and maybe Spurs just decided they wanted to keep him."
Sbragia has identified Saturday's visit of Stoke as his priority, which is why he will hold back key personnel and is hoping Wednesday's tie is settled in normal time.
"I don't want to go to extra time at all so at 75 minutes there may be some strange decisions," the Scot said.
Meanwhile, Blackburn manager Sam Allardyce has expressed relief at retaining Manchester City target Roque Santa Cruz.
"Selling Roque Santa Cruz was something I wanted to avoid and Roque Santa Cruz, with Jason Roberts and Benni McCarthy is a critical area for us to achieve what we want to," Allardyce said.
"We know their goal-scoring power, because it doesn't look like we have many goals from anywhere else, their power is critical for us to get out of this position."
Santa Cruz looks a certain starter against Sunderland but Allardyce is likely to rest David Dunn and McCarthy. Danny Simpson, on loan from Manchester United, may take the place of Brett Emerton, who is out until the end of the season.