A Nine report claimed Cripps and popular defender Sam Docherty stayed away from the team hotel ahead of the Blues' loss to Sydney at the SCG on Friday.
But the reigning Brownlow medallist said he stayed on in Sydney on Saturday night with his wife Monique, arriving back in Melbourne 24 hours after the rest of the playing group did.
"I can cop criticism about form and losing but when it's factually incorrect and questions my character and commitment to the team it p***es me off," Cripps posted on Instagram on Tuesday.
"This is the accountability as players that we would love to see with certain people in the media.
"For clarity for everyone, I stayed with the team the entire time they were in Sydney and joined my wife and family members on the Sat night as we had the weekend off.
"We aren't where we want to be as a team right now, but never question my commitment to this team or club."
It comes as Carlton's once-promising campaign plummets further after losing six of their past seven games, with their only win during that period coming against historically poor last-placed West Coast.
On Monday, the club confirmed board member Craig Mathieson had quit with immediate effect.
Unconfirmed reports suggested his resignation followed an argument with Carlton president Luke Sayers in the Blues' change rooms after the defeat to the Swans.
Carlton have another tricky period ahead, starting with Friday night's match against Melbourne coming off two-straight losses.
The Blues then clash with in-form rivals Essendon, followed by a danger home game against Gold Coast.
Mathieson's uncle Bruce is a long-time Carlton powerbroker and a fortnight ago he fiercely criticised the club administration.
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