Martin O'Neill's men are currently third in the table and seven points ahead of fifth-placed Arsenal, while they are also still challenging for the UEFA Cup and the FA Cup.
Barry accepts that Villa are inexperienced in terms of fighting for silverware but he has called on his team-mates not to throw away all their good work.
"The players in the squad, me included, have not been used to pressure games late in the season," he said.
"Aston Villa in recent years have not been challenging for the league so it is a big ask.
"The big question is, can we continue? But the confidence is there.
"To prove ourselves as a team we have to win a trophy.
"You always go into every season trying to win something and this season is working out nicely for us."
Barry thinks O'Neill deserves great credit for creating such a positive team spirit at Villa.
He said: "I am confident that we can achieve something. There is a great belief in the side and that comes from Martin O'Neill.
"He gives the players a lot of respect and makes us believe we can go out and beat anyone on the day."
Prem 2008/09 Win Outright: Aston Villa 33/1