Grabban came closest to scoring the winner too when he hit the post in the second half, but Huddlestone - who was making his second debut for the club - believes that his side were worthy of a point from the game.
"Sunderland had a couple of chances in the first half and Scott Carson had to play well and we were probably lucky to go in 1-1 at half time," he told Sky Sports News.
"It's honours even and probably a fair result. We have a lot more in the tank. We can press and play better than we have shown today."
Derby are now winless in their last 14 visits to Sunderland, stretching back to December 1990.