“In football today the details make the difference. In every game, some moments are really balanced and you have to try to do something different to achieve what you want - to win.
“Everything is new now but we’re working hard to improve every day. We have a lot of things to improve on but I’m happy, and the players have to be happy as well.”
Silva stepped out at Goodison Park to a standing ovation ahead of a pre-season friendly against Valencia earlier this month and received another rousing reception from the home faithful as he took his seat ahead of kick-off.
An anticipative sold-out crowd then saw their team take the initiative from the off and head in at the break fully deserving of their two-goal advantage.
Silva had vowed to build “something special” for Evertonians in the build up to his side's Goodison opener and praised their role in helping deliver the maiden win of his Blues reign.
“Everybody is happy because it was an important victory for us,” said Silva. “It was a good performance in some moments of the game as well. The atmosphere inside the stadium was fantastic and, overall, for our first match, it’s really good.
“It was fantastic [to have that support]. That was something I expected.
“I know at this Club it is normal that there is a fantastic atmosphere during the matches. [The fans] know, because I already told them, that it’s important for me and the players to feel them behind us, always supporting our players.
“Even in some moments of the game that you cannot perform well, it is important to have their support every time.”
Richarlison followed up his two-goal display on his debut at Wolverhampton Wanderers with another industrious showing, capping his own Goodison bow with what proved to be Everton’s winner.
Last season, the 21-year-old netted five times in his first 12 Premier League appearances while working under Silva at Watford.
And the Portuguese says his summer signing can only take encouragement from another speedy start this time around.
“It’s important for him,” said Silva. “I don’t like to talk about individual players every time - for me the most important thing is always the squad.
"But, of course, two games and three goals is important for him, like the first goal of Theo’s was also important.
”It’s important for all our forwards, for all our players, to contribute goals and get confidence from that."
One blow for Everton saw midfielder Morgan Schneiderlin limp off shortly after assisting Walcott’s opener.
The Frenchman will now be assessed by Club medics at USM Finch Farm.
“I hope it’s nothing serious,” said Silva. “We’ll see in the next few days how he reacts.”