City secured top spot at Christmas for the first time since 1929 with a convincing 3-0 defeat of Stoke at the Etihad Stadium on Wednesday night.
Roberto Mancini's side have dropped only seven points since the season began and scored an impressive 53 goals in their 17 games. Sergio Aguero, the Argentine, scored two in the victory over Stoke, and Adam Johnson scored the other.
Despite the resounding victory, arch-rivals Manchester United remain just two points behind and Barry, currently enjoying a good run in the side, concedes that City cannot afford to ease up.
"At the moment things are going really well," Barry told City TV. "We have set a fast pace in the Premier League but we are still only two points clear at the top. That shows us that there are still other good teams around.
"All the time we are top we know it is in our own hands and we will keep trying to win games."
Barry has been highly influential in City's blistering start to the campaign and has been a regular in midfield alongside linchpin Yaya Toure.
Mancini, with a wealth of talent at his disposal, often juggles his side, but the 30-year-old England international has now started five games in succession.
Barry said: "I feel really good at the moment, really fit. It's good to get a good run in the team because the players we have in the squad, it is sometimes hard to get a constant run.
"But when you are playing regularly that obviously helps you. I am really enjoying my football at the moment."