A New Year's Day contest low on quality saw Jamie Vardy slot in a 58th-minute winner as the Foxes punished Michael Keane's mistake.
Everton's disappointing display featured only two efforts on target, with the first not coming until the 75th minute, and there were boos from the stands when the final whistle confirmed a fourth loss in five matches.
Toffees boss Silva, whose side are 10th in the Premier League, said: "When you didn't achieve, you have to react and we have the quality to react and play better than we did this afternoon.
"We played four games in 10 days, it is really tough, even if you change players. It is not easy to see the players fresh with high mobility every time.
"And when you play against these type of teams, that come here and are waiting for your mistake, you have to put high intensity and mobility in your game.
"But it is not reason to (play as they did). We are playing at home, our fans were, until a certain moment, behind us, pushing our team to win, and I cannot find - but I will find, for sure - the reasons to (play like) that."
Silva felt his players had been "too nervous and anxious."
He said: "It's a disappointing result for us and a poor performance also.
"We missed some of the most important things in football, to pass the normal pass and to do the easy things.
"The first half, even when we were in control of the game, when we won some balls, afterwards our decision wasn't the best.
"I felt our team was too nervous and anxious, without reason."
Silva added when asked if he was worried about his players' mental strength: "You are working in Everton, it is a big club and there is pressure to win matches, to react. You have to show the capacity to handle this type of normal pressure."
Leicester, who rose to seventh, have also beaten Chelsea and Manchester City in their last four games, as well as losing 1-0 at home to Cardiff.
Boss Claude Puel has been ranked among the favourites with bookmakers to be the next manager in the division to leave his post, and a report on New Year's Eve linked Newcastle's Rafael Benitez with Leicester.
Puel said: "I am not sure how that works, putting a bet on. That is not my concern. The most important thing is to show our quality.
"I am just a person who serves the club, that's all, and I would like to continue this way.
"I cannot have an opinion about people outside the club. About our fans, the squad, the club, the directors, staff, it is always the same way, with stability, without problem.
"There is speculation, I don't know why, but it is not my concern."
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