Froch was interviewed by Radio 5 Live the morning after his British compatriot suffered the third professional defeat of his career.
Several media outlets reported the three-time super-middleweight world champion, who won the IBF crown with a stunning fifth-round stoppage of Lucian Bute in May, said Khan should think about retirement following the loss.
But the 35-year-old is determined to set the record straight after Khan said Froch "should keep his opinions to himself".
"I did an interview on Radio Five and my quote was taken out of context on the BBC website on their news pages," Froch told Boxing News.
"I didn't say 'If I was Amir I'd retire,' I said, 'If it was me, I'd retire.' I'm 35 years old, I'm three times world champion, if I'd have lost like that, I would have retired.
"I don't think Amir Khan should retire! That's ludicrous. Why would I tell a 25-year-old to retire?
"Now Amir Khan has read a false quote and come back and said something silly. But I don't hold that against Amir at all. He was just reacting to a misquote."
Froch, who is set to defend his title in November, has no ill feeling towards Khan and hopes he can bounce back from the upset defeat.
"Good luck to the kid, I'm behind him every time he steps in the ring," Froch added. "He's a British fighter and he does British boxing proud.
"The more world champions we've got it's better for our sport, it's better for the attention around what we do, around what I do for a living. We need Amir Khan to win titles, we need positivity around the sport. We don't need negativity and we don't need bad press."