Silva hopes the scrappy 2-0 victory over Bournemouth, who like the Toffees are on a worrying run of form, will provide the confidence boost needed to kick on for the rest of the campaign.
Everton had won just once in eight league matches going into the game so getting back on track was vital to prevent frustrations growing further.
He said: "I was pleased with the result but more the character and personality the team showed.
"It is like an obligation for us to win again at home - not just because of the three points but after our last four matches at home.
"It was something we had to do and we did, by showing strong character and strong personality on the pitch."
The clean sheet was Everton's first at Goodison Park since they beat Cardiff on November 24 - a run of 10 matches - and Silva believes that can also be significant.
He added: "When you don't score more goals, the game is always open but when you can achieve a clean sheet and win the match it boosts our confidence as a team."