The Blues had more than twice as many shots as the Foxes and enjoyed a greater share of possession - but Jamie Vardy’s 58th-minute strike proved decisive at Goodison Park.
The result was Everton’s second 1-0 reverse in three days, with those setbacks coming after a stunning 5-1 triumph at Burnley on Boxing Day.
Boss Silva admitted the Toffees did not come close to hitting the heights they were capable of against Leicester and says his side must showcase their quality every time they step onto the pitch.
“If you look at the past performances and results, we haven’t been consistent,” he said.
“This is the moment to be honest and look clearly at the game, to analyse the match, and pass the feedback to our boys
“I felt our team was too nervous in some moments in the match. We did not put our game out there.”
Everton were the more threatening side in the first half and went close to breaking the deadlock on 19 minutes through the impressive Jonjoe Kenny.
The full-back unleashed a rasping first-time drive that had Kasper Schmeichel beaten all ends up – the upright came to the Leicester keeper’s rescue, though, and the visitors survived.
And it was the Foxes who were to make the breakthrough 13 minutes after the break. Vardy raced onto Ricardo Pereira’s through pass before placing a pinpoint finish past Jordan Pickford.
The Blues worked hard as they searched for an equaliser, with substitute Cenk Tosun twice forcing fine stops from Schmeichel.
In total, Everton fired in 17 shots to the Leicester’s eight but the visitors’ rearguard held strong to see out the victory.
Boss Silva says his players must display more creativity in the final third, as they seek to carve open stubborn opposition sides at Goodison.
“We knew before the match what they [Leicester] came here to do,” he said.
“We know, because of how they respect us, how they will come here to play. They started the game with a 4-5-1, blocking the space and waiting for our mistake.
“We made a mistake and they scored in that moment, which made things more difficult for us and after that we didn’t create the good moments to change the result for us.
“But we have the quality to do different things in our attack, to show more creativity. We have players to do that.
“This afternoon wasn’t the best for some of them, but it is my job to work with them and pass this confidence to them.”
Silva did reserve praise for Kenny, who stepped into the team admirably in what was his first Premier League start since the reverse fixture against Leicester – a 2-1 victory for the Toffees at the King Power Stadium on October 6.
“He did well,” Silva said. “He created some good deliveries and had the biggest chance we had in the game. He helped the team.”