Djukic, who took over from Ernesto Valverde this summer, guided Valencia to victory against Malaga in their Primera Division opener but then saw his troops suffer four successive defeats.
In La Liga they were beaten 3-1 away by both Espanyol and Real Betis while also losing 3-2 at home to Barcelona. The most chastening loss, though, came last Thursday when they suffered a 3-0 Europa League mauling by Swansea at the Mestalla.
That increased the heat on Djukic heading into this weekend's league clash with Sevilla but a 3-1 victory on Sunday night eased the pressure and the former Yugoslavia international subsequently received the backing of Valencia president Amadeo Salvo.
He told Canal Plus: "He (Djukic) will finish the season whatever happens. He has signed for two years with us and the normal thing would be that he completes his contract. I'm convinced about that."
Salvo later added on Onda Cero: "Djukic is our coach and he would still have been even if we'd lost. Djukic said that being the coach here fulfilled a lifelong dream, that deserves respect.
"You need to give things time, there's no need to rush, and in this case we're not going to. We have to invest in things that in the future will give us results."