Steven Naismith, on his 27th birthday, scored the only goal seconds before half-time at Goodison Park and despite Chelsea creating a number of opportunities prior and after they could not find a way through.
Experienced forward Samuel Eto'o had a debut to forget as he missed a couple of chances and was denied a certain goal by a last-ditch tackle from the excellent Gareth Barry, also making his first appearance having joined on loan from Manchester City.
"We didn't score goals. We had chances and chances but we didn't score," said Mourinho.
"If you don't score, what you create means nothing. It is a simple story. Artistic football without goals is not good.
"This was the game when we had 21 shots, nine attempts on target and well before they scored the goal we had easy chances to score.
"I don't think it is a question of sharpness. If the ball to Eto'o from (Andre) Schurrle is sent as a slow pass and Eto'o waits for the ball Barry has time to come.
"If it is a fast ball Eto'o scores with an open goal - I don't think this defeat is about sharpness.
"Perhaps there was not the killer instinct: one chance, one goal. Maybe one day we will have three chances and score three goals and win 3-0."