Partizan's traditional city rivals Red Star took advantage to cut their advantage at the top of the 16-team first division to eight points with a 1-0 home win over Spartak Subotica.
Grant, who steered Chelsea to the 2008 Champions League final after he took over from Jose Mourinho, saw Partizan fall behind at lowly Novi Pazar when striker Admir Rascic headed in an Emir Lotinac cross from the right.
Senegalese striker Lamine Diarra equalised with a clever backheel shortly after the break but Partizan's tepid overall performance left Grant unhappy.
"We came here to win and didn't do what we should have done," the Israeli told a news conference.
"We didn't play well in the first half and we will have to play a lot faster to break down teams as defensive as today's opponents, although a poor pitch made it difficult."
Red Star also did not shine in front of 40,000 home fans in their first match following the December-March winter break but ground out a barely deserved win thanks to an opportunist second-half goal from Brazilian midfielder Evandro.
The livewire playmaker headed home a close-range rebound after a goal-mouth scramble to rekindle Red Star's hopes of winning their first league title since 2007.
"The fantastic atmosphere and Partizan's slip-up seemed to have given my players a stage fright but they showed character and the win is all that matters," Red Star's Croatian coach Robert Posinecki said.
"We will improve because this team includes many new signings while some of the senior members were a bit flat after being on international duty in midweek."
Red Star visit 11th-placed Javor Ivanjica in the next round while Partizan are at home to fifth-placed Sloboda Sevojno.
