The Whites enjoyed 69% of possession and attempted 21 shots during the game.
After the match, Bristol boss Lee Johnson said that Leeds were the better side of the two, but the Robins should have had a penalty.
In the second half, Bristol City appealed for a penalty after Luke Ayling dived to stop an Eliasson cross. They asked for a handball to be given, but the referee allowed the game to go on.
Johnson said that it was ‘a stonewall penalty’ and they do not deserve the result.
He said to BBC Sport: “We then came into it a little bit more when we relaxed and started playing.