In a game of few chances, Derby's Adam Legzdins was the busier of the two keepers but Saunders felt he should have been celebrating his first win since he took over at Molineux last month.
He said: "I thought we should have won again.
"But we didn't have that killer touch in front of goal today. We made enough chances and got enough balls into the box and we were solid and defended well.
"We did all the basics properly and on another day we win.
"We had a load of half-chances in front of goal and we've headed a few balls back into the middle but just not anticipated.
"That's where you need someone who's on their toes to anticipate and poke the ball in the net. But every point is vital and now we move on to Barnsley (on Tuesday night)."
Commenting on the influence of Kaspars Gorkss, Saunders said: "I knew he would make a difference.
"That's the first building block for me to get us a team that can first of all stay in this league and then try and win it next year."