Emile Heskey hit the post in the first half for the visitors and after the break Stoke's Marc Wilson saw his header hit the bar and deflect clear off Gabriel Agbonlahor.
Dunne told Sky Sports 1: "I think we can be proud of ourselves, we worked really hard.
"We were happy with a point, it's a very difficult place to come.
"It's been disappointing (in previous games) to concede a lot at set plays."
Villa captain Stiliyan Petrov praised Agbonlahor for keeping the ball out from Wilson's header.
"I've been saying a lot about Gabby, this season he has been improving his game. He is working very hard for the team," he said.
"It is a very difficult place to come to. We battled really well today, we battled as a team."
Stoke manager Tony Pulis gave Villa credit for the way they played.
Pulis said: "I thought it was going to be a very tough game. That's their sixth draw away from home this season.
"We didn't get out of the blocks as quickly as we'd like to but we have to give Villa some credit.
"Their two centre-halves, Dunne and Collins, were very good tonight."
Pulis said he hoped Peter Crouch, who missed the game through illness, would be back to face Wigan on Saturday.
He said: "We have to make sure Peter is well. He's such an important player for us. When he's ready we'll play him."
Aston Villa manager Alex McLeish praised his players, particularly those playing with injury.
He said: "I thought the team played well. We had some good moments, passed it quite well and showed some composure.
"If we had a wee bit more finesse in the final third we could have got an even better result."
Heskey was forced off at half-time and McLeish said: "Emile Heskey couldn't go on with his ongoing Achilles problem, he might be out for a while now."
The Villa manager was unsure whether Darren Bent would return from injury to face Chelsea on Saturday.
McLeish said: "I don't know. We thought he was ready for this one.
"He will have a scan in the morning. If there is new fluid we will know it is a fresh injury, if not he will be close (to facing Chelsea)."