With the game drifting towards a goalless draw at Goodison Park, Silva brought on Dominic Calvert-Lewin, Ademola Lookman and Cenk Tosun in an attempt to win the game.
With three minutes remaining Lookman crossed for Calvert-Lewin to head the opener before Tosun drilled home the second two minutes later to secure the Toffees' third straight league win and lift them up to eighth in the table.
"That’s football, it’s our job not just to name the starting XI but during the match as well,” Silva told Sky Sports.
“I’m really happy for them. Cenk has come on in the last two home games and scored two important goals, for us and for him as well.
“I was pleased for Dominic and Lookman because they created the first goal and are working really hard as well to get into the starting XI.
“It’s important for us, now we have solutions on the bench to solve some problems during the match.
"We were too slow in the first half, but we pushed them back in the second half. They missed the penalty, a good save, but in the end I think we deserved the three points."
Silva also praised goalkeeper Jordan Pickford for saving Luka Milivojevic’s penalty at the start of the second half.
"Jordan Pickford has the quality to play at a higher level, like he’s playing now, helping us and the national team as well,” added Silva.
“That moment was decisive and important. He is there to help the team and at that moment he helped.”
Meanwhile Crystal Palace boss Roy Hodgson was left to rue that penalty miss and felt his side deserved at least a draw.
"Two goals in the last few minutes, the first one was the killer. It was a massive blow after defending so well and missing the penalty,” Hodgson told Sky Sports.
"It's hard to stand here as a loser again. I could easily be a winner or at least someone who has coached his team to a positive point. They scored the goals and we didn't.
"I asked them to make certain they gave 100% and matched Everton for commitment, they certainly did that. The mood is very sombre because we were so close to a good result, and nobody could have begrudged us it.
"It was a good penalty save but Pickford also made two outstanding saves in the first half. Penalties do get missed, goalkeepers do make saves. You expect to score them.”
"To ask me to come up with some magic formula to try and win the next few games is an impossible question right now,” added Hodgson.
“Let's hope that on the next occasion the goals go in at the right end for us."