The Stamford Bridge side had missed a host of chances, with Samuel Eto'o and Andre Schurrle particularly culpable, when Steven Naismith headed home the only goal of the game in the 45th minute.
Chelsea pushed Everton back for the vast majority of the second period but could not find a way beyond Tim Howard, despite their possession and the opportunities they created.
Mourinho told Sky Sports: "I don't know if I have to say we didn't deserve to lose, or if I should say we deserved to lose.
"We didn't deserve it (to lose) because we were the best team, because we play the best football, because we dominate the whole game, because we had 21 shots, because we risk everything we could...
"In that sense it is fair to say we deserved to win the game.
"But the other way, a team that has 21 shots, some of them easy shots and easy situations to score and we don't score and we have a mistake in the last minute of the first half...
"Maybe with that I should say we deserve to lose."
Mourinho would not pin the blame on Eto'o, who was making his Premier League debut following his summer switch from Anzhi Makhachkala.
"It was not just him. I think Schurrle has missed three big chances to score, other players also had chances, but I don't like to be critical," he added.
"I prefer to analyse the game with the two perspectives I told you before."
And the Blues boss refused to be drawn on Chelsea's penalty appeal in the second half when Oscar went down following a challenge from Sylvain Distin and Leon Osman.
He said: "If I comment I am punished, if I comment I am criticised, so I prefer not to comment."