Former Preston North End boss Grayson took over at the Stadium of Light in June following the club's relegation from the top flight but was unable to turn around their miserable form in the second tier, guiding them to just one win in 15 league games.
The Black Cats' 3-3 draw at home to bottom-placed Bolton last night proved to be the final straw as Grayson was given his marching orders just 16 minutes after the final whistle.
"I feel for Simon, he is a tremendous manager with a great record if you look through his career," Parkinson is quoted as saying by the Sunderland Echo.
"Anybody who came into this club was going to find it a tough challenge to turn it around, I have had it at Bolton last season.
"Changing the mentality around is difficult, he has obviously found it tough but will be back in management sooner rather than later. There will be a lot of people who will want him on board, for sure.
"I just shook hands with him at the end. We normally go for a drink with the opposition manager but we will get on the coach and I will give him a call later in the week."
Next up for Sunderland is a tough trip to seventh-placed Middlesbrough on Sunday.