Arsenal goalkeeper Wojciech Szczesny made the claim last week.
But Terry insisted: "We win and lose together at this club - we're all responsible for the results we have.
"As for the senior players running this football club, that's nonsense. That's just the perception from outside. Roman and the board make the decisions.
"On the football pitch, that can affect what happens upstairs of course. If we don't win matches, the board step in.
"People speculating from various different clubs or previous managers, that's complete nonsense."