Los Blancos defeated Manchester United but it took a controversial sending off of Nani to swing the tie in the Liga giants' favour.
However, although Hamit admits Jose Mourinho's men are a quality side, the midfielder is optimistic about the Turkish champions' chances.
"They've eliminated Manchester United. They were a little lucky but in any case nobody can question Real Madrid's ability," the 30-year-old told reporters.
"They are the favourites of this draw but I think there's a probability that we can do it. It's not that bad this draw."
The Turkey international spent one season in the Spanish capital before moving to Istanbul in the summer of 2012 and is quietly confident ahead of the tie as long as they get off to a good start.
"I'm happy to have the occasion to meet Mourinho and my former team-mates. If we get a good result from the first leg, then we know what we can do in front of our supporters," he added.
"First comes the league for now. Then we'll concentrate ourselves on Real Madrid. I'm in a positive mood."
Gala face Kayserispor on March 17 and are four points clear at the top of the Turkish league.
The first leg of the quarter-finals is on April 2 in Madrid before the return leg on April 9.