Ancelotti is again under intense pressure after defeat at home in the LaLiga to Valencia last Saturday and at Arsenal in the Champions League in midweek.
Bordalas, ahead of tomorrow's clash with Las Palmas, was asked about Ancelotti and said: "You know I'm fond of him.
"I don't understand why there's any criticism. I think he deserves the utmost recognition because he's given so much to Madrid. He can't be questioned. I can't understand it, and I don't agree with it at all.
"He deserves a monument, because what he's done and is doing is unparalleled."
Bordalas was also asked if Getafe receives the press the club deserves for it's time in LaLiga.
He added, "I suppose there will be recognition for being in the Primera Division for 20 years. It's clear that the leading figure is Ángel Torres; he got us promoted to the Primera Division and has kept it there for so long. Now it's our turn, but I think there is recognition for the work we're doing.
"We were in all the odds to be relegated, and fortunately we have 39 points. We want to stay in the Primera Division for another year."