A pair of first-half goals each for James Rodriguez and Alvaro Morata ensured Zinedine Zidane's team made light work of their relegated hosts on Saturday and moved level on points with league leaders Barcelona, on whom they have a game in hand.
Casemiro said the win at Granada was hard-earned, telling reporters: "There are no easy games. We made such a strong start.
"We're not looking at what Barcelona do, we're looking at what we do. It's still down to us.
"It's in our own hands and we know if we win all our own games we will be champions.
"There's no better way to be than depending on yourself."
Zidane rested the likes of Toni Kroos, Luka Modric and Marcelo at Estadio Nuevo Los Carmenes, but Casemiro denied the line-up in Granada was a weakened one.
"In football, the Champions league semi-final does not allow you to relax. If we do that, Atletico Madrid will cause some harm," he said.
"We have to go out hard and try to win the second leg as well.
"There is no B-team here. We know there are players who feature less but you can sense we are never less than fully dedicated.
"We had a good game today."