Antonio Conte sought to draw a line under his bitter feud with Jose Mourinho on Saturday.
Manchester United manager Mourinho on Friday said he regarded the situation with "contempt".
Chelsea head coach Conte on Saturday said the feeling was mutual and that he would not be losing any sleep over the matter, insisting again he was stopping the verbal sparring.
Asked about Mourinho's "contempt" comments following Saturday's goalless draw with Leicester, Conte said: "I think that I said (I'd) stop the story.
"But it (contempt) is the same for me. I don't know if he said this for me.
"But I'm not worried. I sleep very well."
The two Premier League bosses have traded barbs since the new year after Mourinho's comment that he did not feel the need to behave like "a clown" during games touched a nerve with Conte.
That sparked an extraordinary war of words between the pair, where Conte accused Mourinho of having "demenza senile", which directly translates as senile dementia, prompting the United boss to hit back by appearing to allude to a four-month suspension Conte served in relation to match-fixing.
In that case, dating back to the early stages of his coaching career in Italy, Conte was later cleared of wrongdoing.
Conte responded by accusing Mourinho of being "fake" and "a little man".
Almost a week elapsed before Mourinho next spoke in public, with the United boss trying to move on with his "contempt" remark.
Chelsea are scheduled to play United at Old Trafford on February 25, unless the Blues reach the Carabao Cup final at Wembley on the same day.