The composer's Your Country Needs You TV show picked 2009 entrant and later-Sugababe Jade Ewen, who finished fifth in Russia with a song co-written by Lloyd Webber.
"I don't think there's any point beating around the bush," Lloyd Webber told Radio Times.
"Did you see the Eurovision Song Contest this year? Well, if you had seen it, you might have noticed one thing - I don't think there was one black face on the programme."
He continued: "At the press conference in Moscow, I was asked, 'Why have you brought a black artist?'
"I said, 'Because she is the most talented artist that we had and I think she's a major, major star'. I think we would have come second but there's a problem when you go further east."
Lloyd Webber added: "It doesn't mean that we would necessarily have won that year but we could have come second.
"If you're talking about Western Europe - Germany, fine; France, fine; Spain, fine; Greece, fine; Scandinavian countries, fine. But Ukraine? Not so good."
During the interview, Lloyd Webber also claimed that none of the acts on The Voice UK could sing in tune.