The Cottagers were 1-0 up at Old Trafford and earned a penalty to make it 2-0.
However, David De Gea saved Aleksandar Mitrovic's spot kick and United soon equalized.
"We didn't deserve to lose the game," Silva said to reporters.
“The game changed completely from that moment (the penalty save). We should have reacted in a different way.
“It was a moment for us to show maturity and handle the game differently but we haven't done that.
“The game showed again our quality and what we are doing with these players. All season we have to be really proud of what we did."