Real are preparing for Wednesday's Copa del Rey last 16, second leg at home to second-tier Numancia, which should be a formality after they won 3-0 in Soria last week.
"I believe in the work we're doing - I will not throw in the towel", the 1998 World Cup victor said.
Kiko Casilla had to save from Nacho Sanchez and Pere Milla bundled wide as Numancia battled for a second equaliser, before Zidane introduced senior stars Isco and Casemiro in a bid to see the game out.
Zidane admits Real are in a hard situation - and Valdano says the responsibility lays with the coach.
"I want to show that I can also be a good coach in tough circumstances", Zidane said in an article published on Tuesday in France Football magazine, which gives the award.
Zidane added: "When what we want doesn't happen, we have to think about our work".
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"We are recovering things, for me, and we will", he said.
The coach was more than an hour-and-a-half late for his news conference after holding a long talk with his players before training.
Real looked to be heading for a disastrous second league defeat in a row after their embarrassing 3-0 loss to Barca in their last outing when Daniel Wass lobbed over Keylor Navas to put Celta ahead in the 33rd minute. I'm not protected by what I've done as a player at this club.
According to media reports, the club pulled out of a bid to sign French teenage sensation Kylian Mbappe to avoid upsetting Cristiano Ronaldo, Karim Benzema and Gareth Bale, who have only mustered up 10 league goals between them this term. People might think I am not the right person, maybe so, but I believe in what I do.
On Thursday, Levante host Espanyol, Cadiz travel to Sevilla and holders Barcelona welcome Celta Vigo to the Nou Camp.
"When things go wrong, I am not someone to throw two or three players into the s--", he said.