Grayson handed debuts to six players in his first competitive match at the helm, but his side needed to come from behind to earn a point in their first Championship fixture for more than a decade.
The newly-relegated Black Cats were denied a winner by the woodwork in the second half, though, and Grayson believes that there are plenty of positives to take from the season opener.
"I thought we played well. It was always going to be difficult with the hangover from last season but we started the game extremely well and they scored against the run of play," he told Sky Sports News.
"The players showed immense character to get back on it again and we made some good chances. We asked some questions for a good Derby team."
The result means that Sunderland are still winless in front of their own fans this calendar year.