United were second best for large periods against Chelsea, whose dominance was rewarded by Alvaro Morata's superb header in the 55th minute.
Mourinho's side had just two shots on target, with record signing Romelu Lukaku a desperately isolated figure in attack.
Defeat leaves them well adrift of their fierce rivals, who cruised to a 3-1 win over Arsenal earlier in the day, but Mourinho is adamant that their position could be worse.
"We are second not fifth, sixth or seventh," he told Sky Sports.
"There are 18 teams in a more difficult position. Eight points is eight points.
"We went through a very difficult phase with some of the most important matches without important players. It's obvious we've been through a difficult phase with limitations."