Two of the three promoted sides last season, Derby and Birmingham, are currently in the Premier League's bottom three, with only Sunderland seemingly safe having spent over £40m on new players.
Varney added: "With due respect, if clubs like Bristol City or Hull made it, they will give it a go. But they will not spend huge amounts of money to do it. The gap is so big you'll see increasingly that happen.
"If we played Manchester United at the Valley on a Wednesday and Wigan Athletic on a Saturday, we would now in the future play a weakened side against Manchester United because we would see the Wigan game as being the vital game in terms of the league that we are really playing in."
Varney steps down from his post as chief executive in the summer after 11 years in the role.