The visitors enjoyed a dominant first half in which they created the best chances, and they may have felt aggrieved not to have gone in ahead at the break.
Antonio Conte thinks other players are also to blame and not just striker Alvaro Morata for Chelsea's failure to score in their 0-0 draw with Leicester City on Saturday. "We suffered a lot in the first half and at the start of the second half", Conte said.
Conte says our attacking struggles are down to the whole team and not any one individual.
However, although Conte admits he is a huge admirer of the England worldwide, he says that Chelsea are not considering a move to sign him.
Mahrez thought he had should have had a 55th-minute penalty after he tangled with Andreas Christensen, on for the injured Gary Cahill, although referee Mike Jones seemed to have made the right call to turn down the Algerian's appeal.
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.
"We played with tiredness today", Conte said.
However, their comments have acquired more bite lately, beginning when Mourinho implied that Conte was a "clown" for his dramatic touchline celebrations, although he later claimed he was not referring specifically to the Italian.
Chilwell was booked for a foul on Willian, and five minutes he later picked up his second yellow card after catching Victor Moses.
Meanwhile, Abdoulaye Doucoure scored a controversial last-minute equaliser to secure a 2-2 draw for Watford as Southampton's Premier League winless run was extended to 10 matches.
Crystal Palace continued their remarkable recovery under Roy Hodgson as they moved up to 12th in the table with a 1-0 victory over Burnley thanks to Bakary Sako's goal.
Antonio Conte's side welcome the Canaries to Stamford Bridge on Wednesday night before travelling to Brighton & Hove Albion in the league next weekend.