Ryan sparked controversy last week when he wrote "who cares" under a post on the Supercars Facebook page about DJR Team Penske drivers playing cricket at a sponsor event in Darwin.
That prompted a response from DJR Team Penske boss Ryan Story, who wrote "we all work hard to activate value for our partners so we can keep going racing" and added "I would never post a comment like this on a similar Erebus initiative. Never."
The comments were quickly deleted, however the exchange went public over the weekend courtesy of a story in The Daily Telegraph newspaper.
Klimenko addressed the issue on her public Facebook page today, apologising to DJRTP for the comment along with a plea for fans to stop what she says has been "cruel" backlash directed at her team.
"I would like to send my apology to all DJR Team Penske crew, drivers and fans alike," she wrote.
"The statement 'who cares' was uncalled for, and the appropriate apologies have been sent. I have communicated with Ryan Story and the matter has been put to bed. 'Who cares' was an internal joke that slipped out of the bubble, and as a team we are very sorry for this.
"But what I am not sorry for is my team, my drivers or my fans. My team do not deserve the cruel statements being said about them on Facebook, I do not deserve the cruel statements said on FB.
"I wear big girl pants, and I can take what ever you say about me. But my team [has] been traveling since July, going from one isolation bubble to the next. They have not seen their families, and won't see them [until] mid-October.
"So to those who want to say something, or put my team on the chopping block, say it to me. Put it on this page with your name.
Klimenko also fiercely defended Ryan in the post.
"As far as Barry Ryan is concerned, he is a man with a heart of gold," she wrote.
"He cares about his team and left his wife and daughters to make sure this sport keeps going, for you.
"He cares about his team and drivers, he sacrifices for his team and drivers, and if he is a bit rough around the edges, a bit loud or crass, or whatever it is that pisses you off, then deal with it.
"The man saved my team when it needed saving. He picks me up every time I am thrown under a bus. He has more strength and humility than most people.
"This is the man who delivered shields to hospitals while most sat at home safe in their bubble, this is the man who behind the scenes works tirelessly to make this sport more affordable.
"So unless you walk in his shoes, deal with what he deals with, I would appreciate it if you would throw your comments my way, and let the man get on with his job."