There were few chances in the goalless encounter, although Sunderland's Emanuele Giaccherini missed an open goal before half time when it was probably easier for the Italian to score.
"It is a good point for different reasons. We performed for 90 minutes, we made it difficult for Villa and created chances. We are keeping on growing," Poyet told BBC Sport.
"We had a miss from two yards and hit the crossbar. Sometimes you have to understand when you are at the bottom that things don't go for you.
"I think we deserve it (the win). The players were believing. We didn't get the three points but it is a step in the right direction. The idea is to maintain this level and I am sure we are going to be alright."
Sunderland move off the bottom of the Premier League table into 19th position following the result.