The Brazil skipper was left distraught after Netherlands beat his side 3-0 in the third place play-off on Saturday to cap a disappointing World Cup campaign
The Selecao had been favourites to win the tournament on home soil, but were thrashed 7-1 by Germany in the semi-finals before losing the consolation match to the Dutch.
And Silva insists his team deserved better than conceding 10 goals two games and settling for fourth place.
"We are frustrated. We dreamed of this moment," the Paris Saint-Germain star told TV Globo.
"I barely slept last night and for it to end like this.... We didn't deserve this ending. Unfortunately that's football.
"We have to apologise to those who supported us against Germany and Netherlands. They booed us at the end, but that's completely normal because they have feelings too.
"It's a big disappointment to go home and tell your family that you didn't make it. It's tough."
Meanwhile, Oscar admitted he was deflated by the defeat, insisting the whole team was left "very sad" by the ending to their campaign.
"It's a terrible feeling. There are no words to describe it," he added.
"We suffered a big defeat against Germany that no-one expected and we came on the pitch trying to get third place, but it wasn't our day.
"We created some chances and played fairly well, but lost. There's nothing left to say. We have to look at our mistakes and plan for the future.
"We conceded a goal within two minutes and that makes things hard for you. Everyone is very sad. The Brazilian people are sad as well. But we tried until the end, unfortunately we couldn't finish with a win."