Aston Villa's Libor Kozak in action with Derby's Will Hughes
Villa created numerous chances against the Rams in the first half, striking the post twice through Gary Gardner and Ross McCormack.
But the home side came out the stronger in the second period, with Tom Ince forcing visiting stopper Gollini into action but Richard Keogh had a header cleared off the line, and then Hughes reciprocated by doing the same to deny Villa's Tommy Elphick.
Aston Villa's Ross McCormack struck the post in the first half
And on reflection, Will Hughes believes a draw was fair result.
"I think the draw was probably a fair result in the end,
"They will look at it and think they could have had the three points.
"They hit the woodwork a couple of times and created a few other chances but I thought we came back into it in the second half.
"We did well, created a few chances of our own, which could have gone in on another day."
Pierluigi Gollini of Aston Villa collides with Chris Martin of Derby County
Derby have been impressive defensively so far this season, and another clean sheet for Scott Carson means the Ram have only conceded in one competitive fixture this season, that coming against Barnsley in their second game of the season.
Villa meanwhile have had a steady start to the campaign, sitting 12th after four games with five points.
The result was Derby's second 0-0 of the season