The Black Cats could take plenty of positives from the encounter but there were reports of a disagreement between Dossena and Bardsley, who allegedly kicked out at each other.
Commenting on the incident, Poyet said: "I didn't see it.
"(But) I like that, if it doesn't go into personal, I like a bit of tension in the team, it's nice, especially when we are down at the bottom. You need a little bit of tension, discussion and characters."
In stark contrast to the Black Cats' recent home form since taking charge, Poyet had overseen three away defeats which contained three red cards and three own goals prior to the trip to the midlands.
But the point against Villa has taken his side off the foot of the table.
And he was quick to salute his side's display.
"This was without any doubt our best performance away from home," he added.
"We made it difficult for Villa, we were brave on the ball, we created two or three chances. For a team at the bottom, playing away from home at Villa Park, I don't think it's too bad.
"We would have liked three points but I want that team on the pitch every week. And if we play like that we'll win plenty of games."
- Sports & Recreation