The 53-year-old was announced as Joaquin Caparros' replacement on Thursday and has signed a one-year deal, with an option to extend further.
Levante finished 10th last term and although the new coach is keen to continue their development, he is also aware preserving their top-flight status is the top priority.
"Levante is a serious club, for sure, they know what they want, what they have, and that's important," he said at a press conference on Friday.
"The last three coaches have done well. The stakes were high and they did it or equalled it. I hope I can too.
"I hope I can reciprocate the trust they have put in me. It's true that since they came up they have had some very good seasons and hopefully it stays that way."
The role is Mendilibar's first in football since being sacked from Osasuna in September last year.
