The Clarets are currently second in the Championship with 76 points from 37 matches, 10 points clear of third-placed Derby County.
Sean Dyche's team could further increase their advantage and consolidate their place in the second and final automatic promotion spot with a home win against Doncaster Rovers on Tuesday.
However, Barnes insists that he and his team-mates are not thinking too far ahead into the future and are taking it one game at a time.
"It's just about the next game, that's all it is," the 24-year-old told the Lancashire Telegraph. "After tonight it will be Saturday - it's always just one game at a time.
"The group has been relentless since I arrived. It's a massive word among the camp and we use it nearly every day in every sentence. That's what we need to be again.
"We will only talk about the Premier League once it has happened."
Barnes joined Burnley from Brighton & Hove Albion in January and scored his first goal for the Lancashire club in their 3-0 away win against Charlton Athletic on Saturday.
He now hopes to bag more goals and help his side gain promotion to the Premier League.
"Getting the goal was probably a bit of a weight off my shoulders," said Barnes. "You could say there's an expectancy when I'm filling in for Danny (Danny Ings), but I'm here to play my part.
"I've come in and hopefully I can score as many goals between now and the end of the season.
"The main aim is to score goals. Everyone will look at me and think about goals. Hopefully I can get on the scoresheet again.
"I can relax a bit more now and hopefully crack on and get a few more."