Conte was speaking following Chelsea's 0-0 draw with Leicester City on Saturday, the first time in the club's history they have been involved in three successive goalless matches.
"Leicester had a lot of chances in the first half, and we did not respond until the second half when we brought on fresh faces, which led to good chances".
Antonio Conte blamed tiredness for Chelsea's lacklustre performance in their 0-0 draw with Leicester at Stamford Bridge. "In the first half and in the first 15 minutes of the second half we suffered a lot".
As things stand on the point tally, Chelsea are now on level terms with second-placed Manchester United with the Devils yet to play a game.
The Foxes dominated possession for large periods of the encounter and created the better chances than the home team.
Conte has also criticised United's spending, while Mourinho even mocked the Chelsea head coach for having a hair transplant.
July 2017: After Chelsea won the title, Conte said: "Two years ago Chelsea finished 10th".
When Gary Cahill was taken off injured, there might have been some small part in him that was grateful he did not have to deal with Jamie Vardy.
However, recent reports suggested the Blues are struggling to make headway, with Juventus refusing to drop their £60million valuation of the player.
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".
Chilwell was booked for a foul on Willian, and five minutes he later picked up his second yellow card after catching Victor Moses.
Abdoulaye Doucoure's controversial last-gasp equaliser denied Southampton a first win in 10 matches, with the midfielder diverting the ball in with his arm a minute before fulltime as hosts Watford came from two goals down to snatch a 2-2 draw.
Chelsea got the better of the Red Devils in their first Premier League meeting of 2017-18, winning 1-0 at Stamford Bridge.
"We have to try to improve in this aspect, but the problem is not just for Morata, or [Michy] Batshuayi when he plays".