Manchester United were destroyed 4-0 by Chelsea at Stamford Bridge, which left Manchester United with just one league win in their last six matches.
The Red Devils, who appointed Mourinho in the summer, are currently seventh in the league table, six points adrift of the top three, consisting of Manchester City, Arsenal and Liverpool.
In his programme notes, Mourinho wrote: “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.
“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.”