Madrid head to Turkey in desperate need of a victory after one point taken from two games has left them sitting bottom of Group A and facing a fight to make the last 16.
A surprise league defeat by newly-promoted Real Mallorca on Saturday has put the pressure back on Zidane, who led Madrid to three consecutive Champions League triumphs in his first spell in charge at the club.
"Football forgets what you've done in the past, that's life," Zidane said at a press conference in Istanbul on Monday.
"And for me it's the same, it's all about the present. The past is the past.
"I'm not going to tell you that what they say doesn't bother me because it bothers me but I can't prevent people giving their opinions. This is a big game in a big stadium and we know the situation."
Eden Hazard is available again after missing the game against Mallorca following the birth of his fourth child and Toni Kroos is also in the squad after recovering from injury.
But Gareth Bale and Luka Modric have not travelled as they are still suffering from calf and thigh problems respectively.
Some reports in Spain have even suggested Zidane could be sacked if Madrid fail to deliver on Tuesday.
"I don't know, you have to ask other people about that," Zidane said. "I want to be here forever but the situation can change."
Despite their bumpy start, Madrid's loss to Mallorca was their first in La Liga this season as they sit second in the table, one point behind Barcelona.
"Everyone knows that the squad is with Zidane to the death, no matter what," said captain Sergio Ramos.
"We have to show we are a united team and one that continues to trust its coach. Madrid always responds and the way to do it is together."
Jose Mourinho has again been mentioned as a potential successor to Zidane.
"We only think about winning tomorrow, nothing else and not what certain people claim," Ramos said. "It is true the measuring stick is sometimes different depending on what it measures."
Ramos added: "It would be easy to say Zidane will stay until the end of the season and there would be no arguments. I know that rumours are interesting for the press but talking about possible coaches is tedious."
Zidane said nothing surprises him about the pressure he is under. "It's always like that," he said. "I've spent 18 years here and the same thing happened to me as a player.
"I know where we are and that there is going to be pressure. The only thing is to prepare for the game but whatever happens tomorrow is not going to change anything."
Galatasaray also have one point in the group after they drew away at Club Brugge and lost at home to Paris Saint-Germain.