The Mestalla club have won just one of their last five games and Wednesday's defeat to Almeria was greeted by widespread shows of dissatisfaction from the club's supporters.
Djukic's charges were booed from the pitch, while fans waved white handkerchiefs - a traditional Spanish show of dissent.
The Serb was brought in to replace Ernesto Valverde, who had guided Valencia to fifth, but they currently sit 11th in the Spanish top flight.
He also fell out with key defender Adil Rami, who was suspended for blasting Djukic's poor relationship with the playing squad and has since signed on loan for Milan.
However, the club's hierarchy have put their faith in the 47-year-old, having been through four separate coaches in the past 18 months.
"The board of directors of Valencia expresses its full support for the players, coach and coaching staff of the first team," a statement read on their website.
Djukic will hope to get back to winning ways when his side face Getafe on Sunday.
‘Even though Kevin Keegan was my boyhood hero, we never really saw eye-to-eye. That was an underwhelming time for me – I felt on the outside’: Newcastle cult hero reveals disappointment over how things went under King Kev
Alexander Isak puts uncertainty over his Newcastle United future to bed amid fresh PSG and Arsenal links
