The Spanish giants made the most of home advantage in the first leg of their last-eight clash to surge into a 3-0 lead.
Jose Mourinho's men are now overwhelming favourites to make the semi-finals and edge a step closer to continental glory.
Goals from Cristiano Ronaldo, Karim Benzema and Gonzalo Higuain saw Real make light work of Gala at Santiago Bernabeu on Wednesday.
Alonso admits they will head for Istanbul in control of the tie, but feels they still need an away goal to make absolutely sure of their progress.
The midfielder, who picked up a booking in midweek which will rule him out of the return leg in Turkey, told Sky Sports: "Probably we will have to score one more goal.
"In the first half they had a few chances, but overall we are really pleased with the performance and with the result. We know that over 90 minutes anything can happen in football and we have to be really careful.
"We know that we have a great advantage, but we can't take anything for granted.
"We know that they are going to push really hard, they are going to try from the first minute to score a quick goal and have something to push for. We have to be really focused."