Madrid won both competitions last term and had been expected to dominate again after thrashing Barcelona over two legs in the Supercopa de Espana, but that has not proved to be the case.
Zidane's men are third in the league, eight points off the pace set by Barca, while they trail Tottenham in their European group and have yet to book a place in the round of 16 after defeat at Wembley.
But Casillas - a former Madrid team-mate of the current coach - believes the Spanish giants will improve as the season goes on, insisting they should not be written off in either competition.
"Everyone is waiting for a mistake from Real, but this is a team which has won two Champions Leagues in a row and no one could do that before.
3-1 - Tottenham have inflicted Real Madrid their biggest defeat in all competitions under Zinedine Zidane. Alarm. pic.twitter.com/MzwFeT0BcW— OptaJose (@OptaJose) November 1, 2017
"So apparently they are not in the best shape right now in LaLiga and they have lost a game against Tottenham, but we have to wait.
"There are still a lot of games to come in LaLiga. And it's the same for the Champions League; everything is going to be decided in February."