The Black Cats' 3-1 victory over Norwich City at Carrow Road on August 13 has represented their only league win this season, with the club now languishing in the relegation zone.
Grayson's 18-game tenure at the Stadium of Light was ended after the club drew 3-3 with fellow strugglers Bolton Wanderers, who also have just one win from their 15 outings this season.
"I don't have to explain the horrible start to the season we've had, actually the very start wasn't so bad, but the stats speak for themselves," Short told the Sunderland Echo. "I don't believe that squad of players belongs in the bottom three of the Championship.
"What's worse is that it is not as if we've not been putting in good performances and just can't get the ball in the back of the net, our goal-scoring performance is towards the top of the league, but we've given away more goals than all but one team, with many of the defensive players we had last season in the Premier League.
"That's just not acceptable and our view at the club was that we needed to make the change. Simon [Grayson] is a very good man, he tried his best, we have a lot of respect for him, but we felt like we needed to try and make a change."
Sunderland are yet to appoint a replacement for Grayson ahead of their tie with Middlesbrough on Sunday.