Mourinho used his matchday programme notes to issue the sorry message to supporters ahead of the EFL Cup derby clash against rivals Manchester City.
Mourinho said: “As the leader of this squad I want to start by saying sorry to all the Manchester United fans around the world.
“Sunday’s 4-0 defeat at Chelsea was not a United result; it was a result that has made us all extremely sorry for all our supporters and we all apologise for it.
“Once again our fans were sensational. I cannot think of another set of supporters who would be singing for 90 minutes like that when their team was losing.
“They were a credit to the club and I feel so sorry for them that the result could not match their performance.”
Mourinho added: “Even in the best periods of the club’s history there have been heavy defeats – I have beaten United 3-0 as a manager and 3-1 twice – but we all know that we cannot accept results like the one we had on Sunday.
“There is only one way I know to react to this kind of result and that is with hard work.”
Signing off his message, Jose added: “I will be there with you on the touchline and together we will all support and push our players to give the 101 per cent effort required in this kind of match.”