The Real Madrid boss is expecting a tough encounter with the Turkish champions but is determined to win the first leg
The Spanish champions drew their home encounter with Manchester United in the last 16, forcing them to win at Old Trafford, and the Portuguese is determined not to have to do the same thing again.
"The draw is not something to get nervous about because there is not much to choose between the teams," he told the club's official website.
"It will be tough but we need to try to get something positive from the first match, something we didn't manage against Manchester United. We have to make sure we go there with a small advantage."
Mourinho went on to warn his side not to rest on their laurels after their win against Manchester United and to make the last four of the competition.
"It was a great win, but Real Madrid can never be happy with getting to the quarter-finals and we always have to look to go further. That’s why we are already thinking about making it to the semi-finals."
Madrid and Galatasaray clash in Spain on April 3 before meeting in Istanbul on April 9.