Madrid bounced back from their shock 1-0 home defeat to Real Betis by edging past Alaves on Saturday, winning 2-1 thanks to a brace from Dani Ceballos on his La Liga debut for the club.
However, Los Blancos did struggle during the game as they came under intense pressure with Alfonso Pedraza hitting the woodwork twice in the second half, adding to Manu Garcia's first-half bullet header.
Despite his side's slump in at the start of the season, with just three wins in six league matches, Zidane insists Madrid are starting to turning things around.
"There has to be patience. It's not a brilliant time for us, but we have to accept it," said Zidane.
"I'm certain that we'll have a better performance next time.
"We know that it's difficult wherever we go, Alaves needed the points. They had a good game.
"I'm satisfied and so can everyone be because we got what we wanted, the three points.
"I won't single anything out in particular, but we got the three points and we'll have much better days, especially in terms of our performance, but you have to congratulate the players.
"Playing every three days ultimately requires a big effort, so we can be happy.
"Two goals aren't many for all the chances we had, but the important thing was to win."
Ceballos had reportedly been frustrated at the fact he remained an unused substitute in Madrid's 1-0 home loss to Betis on Wednesday night, but he vented any lingering irritation by scoring the brace which secured the victory for Madrid and drew praise from his coach.
Zidane said: "He's ready to play, he did very well, and both of his goals make me happy.
"The goals aside, he did very well, played very well and I'm happy for him because he's a lad who wants to learn, and he'll get more chances. We got the three points thanks to him.
"I'm happy for Dani, he's done well. He had a great game and showed that he was worthy of being here."
Cristiano Ronaldo didn't get on the scoresheet, after hitting the post with a curling effort, but Zidane insists the Portuguese star is remaining calm despite recent frustrations.
"When he doesn't score, you ask about him, but he's calm," said the Madrid coach.
"He wants to score and had chances to do so. Ultimately, like always, he'll make the difference.
"He likes his position and we can play in different formations. He was our only striker against Alaves, but we can change things on Tuesday."