The La Liga champions were off and running as Belgium superstar Eden Hazard put them ahead inside the opening seven minutes.
Real Madrid dominated the game afterwards and could have extended their lead when Mariano Diaz hit the post few minutes later.
Arturo Vidal was sent off after an argument with referee Anthony Taylor following an incident in which the Chilean thought Inter Milan deserved a penalty.
Real Madrid capitalized on their numerical advantage as Achraf Hakimi scored an own goal in the second half and that was enough to secure Zidane’s men’s second win in the Champions League.
“It was an important game, we prepared it well. We knew it would be tough, but we played with character and had the right approach,” Zidane told Sky Sport Italia.
“I am happy for the players, because they are often criticised when our performances aren’t great. You cannot always win in football, the important thing is to give your all every time and that is what we did this evening.
“We want to always play beautiful football and get the victories, but it’s not always possible. We played very well last week for 75 minutes and then conceded a goal, people act like it’s a disaster. That’s not how football works.
“I am sorry for Inter, as they had played well in the first game, but this is football.”
Zidane was asked for his thoughts following the death of football legend Diego Armando Maradona.
“We are all sad for him and his family. It’s not just those in football, because everyone in the world adored Maradona. I always have him in my mind, as I was 14 years old in 1986, so what I saw him do on the field was unique,” Zidane added.
