The Foxes needed a 97th-minute free-kick from Riyad Mahrez to steal a point at home.
Claude Puel's side travel to the Hawthorns on Saturday to face a relegation threatened West Brom.
"It doesn't matter the opponent," Silva reflected to the club's website.
"We try every game. It doesn't matter who is in front of us.
"We try to win every game and that's what we're going to do. The next game against West Brom and then after West Brom, also until the end."
He continued: "It's not the result that we wanted, but the team continued to go after the score and finally at the end, we got the goal.
"I think we deserved more. It wasn't the result we expect and also what we put on the pitch. The team has a good character and they continued to work hard to come back."