Williams came to the Eagles' complex Monday -- a players' day off -- to meet with Kelly.
"He was frustrated," Kelly said. "I have no issues with Cary. Cary's just a competitor. He always wants to play a perfect game. He'll tell you he just got frustrated."
In the past, Kelly has used Williams as an example of a veteran player who has bought into the Eagles' practice habits and sets a good example. Last week, Williams was limited for two days of practice because of a hamstring issue. He played all 78 defensive snaps against Washington on Sunday.
"A lot of guys coming in here had no legs," Williams said after the game. "We've got to start taking care of our guys throughout the week in order for us to be productive and have more energy on Sundays. You've got to be smart, as a coaching staff and as players.
"I'm just going to be honest with you. It's hard to go out there and fight for 60 minutes when you're fighting throughout the week to make it through one practice. I'm not the only one. I'm just the only one that's man enough to stand up here and talk to y'all. It's obviously, in my opinion, an issue in our starts."
Kelly acknowledged Monday that "we ask our guys to run" more than many other teams. But he said the Eagles, as part of their sports science-based approach, monitor players closely and change their regimen as needed.
"We assess everybody daily," Kelly said. "We monitor every player. It's all done on an individual basis. You'll see some guys who aren't going full on a day and other guys are going full. It's all done on an individual basis. We take care of everybody from that standpoint."
Williams, 29, cited his age as a factor. Kelly, who developed his approach while coaching college players at Oregon, said his staff takes age into account.
"We look at every player as an individual," Kelly said. "What we do with Trent Cole is different from what we do with Marcus Smith. What we do with DeMeco Ryans is different from what we do with Casey Matthews.
"Every player, on a daily basis, the strength coaches sit down with every guy. 'Where are you? What do you need? Is it a hamstring or a hip or a shoulder?' Because everybody is different and there are a wide variety of ages."
Kelly said he wasn't bothered that Williams voiced his concerns to the media.
"You guys are everywhere," Kelly said. "I told him he can [come to me]. Some places, you can't come talk to the coach. My door's always open."