The Stamford Bridge outfit wasted a series of chances with debutant Samuel Eto'o and Andre Schurrle both missing good opportunities to give Chelsea at least a point.
And they were duly punished for not capitalising on those opportunities when Steven Naismith scored a close-range header on the stroke of half-time, after good work from Ross Barkley and Nikica Jelavic.
Chelsea continued to press for the equaliser in the second half at Goodison Park, but could not muster one as Mourinho slumped to his first Premier League defeat since returning to the club.
"We had chances and chances and we didn't score," said Mourinho. "If you don't score what you create it means nothing.
"If you create and score goals you get three points and win the game.
"Perhaps we didn't have the killer instinct, maybe one day we'll have three chances and score three goals.
"The players are good so sooner or later we will score goals related to the production of chances.
"We have to play to our strengths which is what we did, but we have to put the ball in the net."
Mourinho also felt his side should have had a penalty when substitute Oscar was fouled by Sylvain Distin in the second half, but referee Howard Webb waved for play on.
He added: "Normally a top referee, and he is a top referee, a penalty is a penalty. We would have had a good chance.
"If that is not a penalty the one for Manchester United against Crystal Palace is not a penalty."
