The Blues head into the game knowing a win will see them rise to seventh in the Premier League table.
Silva’s side were edged out 1-0 by Brighton & Hove Albion on Saturday, despite carving out several chances and being denied by the woodwork twice.
The manager has now called on his team to display the resolve shown at Burnley on Boxing Day when Everton hit back from a defeat to Tottenham Hotspur to sweep aside the Clarets 5-1.
The Portuguese is convinced a victory against the Foxes at Goodison could inspire a strong second half of the season.
“It’s up to us to win again, not just one game but more games in a row to get this confidence going again and be more consistent,” said Silva.
“When you are consistent with performances you are closer to getting the results you want, I’m sure about that.
“Even if you don’t win every game, if you maintain good performances, you are closer to winning matches.”
Everton fired in more shots than Brighton on Saturday and had a greater number of efforts on target than the home side.
The Blues also enjoyed the lion’s share of possession but, ultimately, Jurgen Locadia’s 59th-minute strike proved decisive at the Amex Stadium.
Silva’s team almost produced an instant response to the Dutchman’s goal – Richarlison’s low drive was palmed onto the post by Seagulls goalkeeper David Button.
Kurt Zouma then planted a header against the crossbar as the Toffees poured forward late on.
The equaliser proved elusive, however, and Silva admitted his frustration Everton could not make their chances count.
“If you look at the match, we didn’t deserve the defeat,” he said.
“We hit the crossbar and the post, too. We were unlucky with the deflection off Andre Gomes [for Brighton’s goal].
“It is football, they were effective and scored the chance they had, even if we had more clear chances to score. It was a tough match with big intensity.”
The clash with Leicester on Tuesday represents Everton’s fourth top-flight game in just nine days.
Silva admitted the punishing fixture schedule has been a challenge for his players but is confident they can dig deep against Claude Puel’s men.
The Blues’ squad could also be boosted by the availability of Ademola Lookman, who faces a late fitness test as he continues his recovery from an ankle injury.
“It’s been tough [the fixture schedule] but not just for us,” he said. “We changed two players [against Brighton from the XI at Burnley], I think they changed one, but we always have to give our best.
“It’s tough for us but it’s tough for all the teams.”