The former Preston North End boss took over at the Stadium of Light in June following their relegation from the Premier League but the side's woes continued in the Championship and Grayson was duly sacked after just one win in 15 league games.
Last month Chris Coleman swapped the Wales national job for the Black Cats, who have since picked up just their second win of the campaign.
"It's not going to be easy," Grayson told talkSPORT of his former side's survival chances this season. "No club has a divine right to stay up and not go down; we've seen in League One Leeds, [Nottingham] Forest and Man City. There's been Sheffield Wednesday and Sheffield United... a lot of big teams have been in League One.
"But I do believe there are a number of talented players who are underachieving at this moment in time, and they need to take responsibility to get the results to get them out of trouble at this moment in time.
"So, one: they need to start winning at home – it's been well-documented it's nearly a calendar year since the last victory [at the Stadium of Light]. I'm sure they know they are in a fight, but I think they have got the quality to get out the trouble."
The North-East outfit are currently 23rd in the Championship table and two points from safety.