Capello's side, who drew their opening Group H fixture against South Korea 1-1, were eventually edged out in a listless encounter on Sunday as substitute Divock Origi struck a late winner.
Russia now likely need to win their remaining game against Algeria and hope other results go their way to progress.
But the former England manager refused to be too downhearted, proclaiming himself happy with Russia's display in Rio de Janeiro.
"We had a chance to score twice, but that's football. The performance of the team was good, I'm disappointed for the players," said Capello at his post-match press conference.
"Frankly, I'm happy with the performance.
"The result is unfair, but we had clear chances to win. Both teams tried to give it their all and win. Unfortunately, it was Belgium who was able to get the win."
So poor was the spectacle that some of the neutral fans at the Maracana resorted to booing for periods of the second half, which flew into the face of Capello's assertion that it was a good game.
He added: "I thought the match was played with great pace and intensity and was a very interesting one.
"Because of this, we made mistakes and so did they."
