Asensio started nine La Liga matches in the first half of the 2017-18 campaign, but has struggled to hold down a regular spot in Zidane's XI since the turn of the year.
Nevertheless, Asensio has still scored 10 times and registered five assists in 40 appearances for the Spanish giants this season.
The 22-year-old has played down suggestions that Zidane has been unfair to him as he targets a regular role between now and the end of the campaign.
"[Unfair] is not the word," Asensio told El Larguero. "Because of issues, he chose others. It was my fault and my responsibility when I was out of the team.
The dynamic of the team was not so good and I did not have so many minutes. I wanted to do everything in the 10 minutes I had. In those moments you have to be mentally strong.
"Now he is giving me confidence. I think that both in attack and in defence we are more compact and we have to continue like this and maintain this line. We are in a very good place."
Asensio is currently with the Spain squad ahead of the upcoming international friendlies with Germany and Argentina.