The Portuguese coach questioned the fitness of his team as they put in a lethargic performance in the 1-0 loss.
Mourinho told Sky Sports: "The struggle started in the way we pressed or, I will say, in the way we didn't press because our pressure up was very poor.
"I would say it was lazy pressure and when you have lazy pressure, you don't press and you let opponents build from the back and then they have players with incredible quality, which is not just Everton, it's almost everybody in the Premier League. When you let them play from the back then they are comfortable with the ball."
The former Manchester United manager feels that the lack of pre-season preparation for his team was demonstrated on the opening day.
Mourinho explained: "I could also feel that some of my players are not fit. Matt [Doherty] was struggling to play the way he plays and the way you want him to play, as an example.
"We also had other players that were a little bit in trouble from a physical point of view. Two very strange pre-seasons for some and in other cases not even a pre-season, but congratulations to my dear friend Carlo (Ancelotti) and the Everton boys."
The 57-year-old coach added: "I couldn't expect them to be sharp, intense, agile. But I was expecting much more individually and collectively.
"It disappoints me, and that is where I have now to work. The players who didn't have pre-season, we don't have now the possibility to give them a pre-season."