The Radio 2 DJ argued that the British entrant never had a chance of winning the competition because Eastern European nations refused to vote for a black singer.
He described Abraham's colour as the "elephant in the room", commenting: "East of the Danube, they won't be voting for a black singer any day soon."
Abraham came joint last in this year's contest, scoring only 14 points. None of the 22 Eastern European entrants voted for him.
Wogan told the Daily Telegraph that the only way Britain could win the music contest again would be if a major recording artist such as Take That, Elton John or Robbie Williams got involved.
"If the British music industry can't swing even one of our major acts to represent the country at the Eurovision, we're really wasting our time," he added.