"It was very hard to win here", Conte stated after the game in his post-match conference.
With Kurt Zouma ineligible to face his parent club and Kevin Wimmer out injured, Stoke fielded a patched-up defence that included Glen Johnson as part of the back three.
Conte said: "Morata played a good game".
Stoke enjoyed a good spell towards the end of the half with Mame Biram Diouf's overhead kick dropping over the bar and Fletcher had an effort blocked on 43 minutes. Stoke remain 15th after a fifth game in all competitions without victory.
Morata's record after six games is six goals and two assists.
He arrived at Chelsea as second choice after top target Romelu Lukaku chose instead to join Manchester United - United had been expected to sign Morata until they were told they could win the race for Lukaku.
Hazard, 26, made his first start of the campaign in the Blues' 5-1 win over Championship outfit Nottingham Forest on Wednesday after making three appearances from the substitutes' bench in the Premier League and Champions League.
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Patrick Reed, Justin Rose, Gary Woodland and Jon Rahm finished Round 2 one shot back at 6 under. Dustin Johnson and Jordan Spieth are four shots back.
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Police have recovered weapons from their possession. "We shall not allow any terror module to come up in Jammu region", he added. "An FIR has been lodged against the assailants and a search operation launched to nab them", he said.
Conte said of the 24-year-old: "I like him because he's a complete player and also he has a lot of room to improve in every situation, tactical, physical, technical aspect, he's very committed, his behaviour is always fantastic".
Chelsea forward Pedro will return to Antonio Conte's squad for the trip to Stoke on Saturday while Tiemoue Bakayoko is available despite being involved in a auto accident on Thursday.
Antonio Conte: "It's normal to come here and suffer".
He added: "We have to play against Stoke then on Wednesday another really important game for us against Atletico Madrid".
Now, Antonio Conte has confirmed that the player is in contention for the game against Stoke this weekend.
While Morata is quickly cementing a standing as the new darling of Stamford Bridge, Chelsea have sanctioned the sale of Costa to Atletico Madrid and he will embark on a second spell with the La Liga giants from January. He nearly notched another couple of goals in addition to his maiden hat-trick for Chelsea, following his club-record switch from Real Madrid.
Alvaro Morata scored a hat-trick in the 4-0 win over Stoke City.