Cattermole believes that it was a fair result on the night, despite Sunderland coming closest to a winner when Lewis Grabban hit the post.
"I thought we started well and conceded against the run of play," he told Sky Sports News.
"It's not easy when you've been relegated and the lads are lacking confidence. I thoughts the lads were brave. Derby controlled a lot of the second half so a draw was probably a fair result."
Sunderland are now without a win from their last 18 league games in the month of August, stretching back to 2010.