Derby and Hull are currently competing for an automatic promotion spot in the Championship, with Middlesbrough topping the division.
Burnley are not too far behind the three promotion-chasing sides though, and Barton wants to see his team keep pace with the front-runners.
"Middlesbrough have pulled away at the top, Hull have done fantastically well and Derby, so it's important that we stay in that group," he said.
At the moment Middlesbrough have a two-point lead over Hull at the top of the table, and they have a game in hand on all the other sides in the top six.
Aitor Karanka’s side look the dominant force in the division, and it could be that Hull, Derby and Burnley all are left to fight it out for one other automatic promotion spot.
The Tigers are currently four points clear of Paul Clement’s side, following Derby’s recent slump in form.
Burnley, meanwhile, are in fourth spot - five points back from the top two - but Sean Dyche’s men have been in impressive form of late.