Roush Fenway Racing filed an appeal on the penalties against Matt Kenseth's team on Saturday.
Evernham said before Sunday's race he was most concerned about the severity of the penalties, particularly the points deductions, and the damage allegations of cheating have done to the reputation of his organization.
"That's been tarnished and it bothers me more than anything," Evernham said.
Kenny Francis, Kahne's team director, was suspended for four weeks and fined $50,000 after NASCAR inspectors discovered that two layers of duct tape covering an air hole near the rear wheel well came off during qualifying.
Officials said the first layer had a razor slice in it that they believe was designed to force both layers of tape off.
Kahne was docked 50 championship points and Evernham 50 owners' points for what NASCAR deemed a blatant attempt to create an aerodynamic advantage.
Rodney Childers and Josh Browne, the team directors for Riggs and Sadler, were suspended for two races and fined $25,000 each when officials discovered the bolts that attach the rear spoiler to the trunk had holes drilled in them to help create an aerodynamic advantage.
Their drivers were docked 25 championship points each.
Evernham said the bolts were hollowed out to make them lighter and were used in all four restrictor plate races last season without penalty.
Kenseth was docked 50 points and lost his crew chief, Robbie Reiser, for four weeks after officials discovered caps covering the rear wheel-well hole had come off during qualifying.
Roush Fenway Racing president Geoff Smith said his appeal is aimed primarily at reducing the points penalty.
He noted Jimmie Johnson was not docked points last year when crew chief Chad Knaus was suspended four weeks for rigging a device to raise the rear window of Johnson's car during qualifying.
NASCAR officials said a date for the appeal, to be heard by the National Stock Car Racing Commission, has not been set.
David Newton covers NASCAR for ESPN.com. He can be reached at firstname.lastname@example.org.