The first-half finished 1-1 after Hertha took an early lead when Grujic, on loan from Liverpool, volleyed into the top corner with nine minutes gone.
The hosts fought back and equalised when defender Lukas Klostermann headed home a corner with 24 minutes gone.
The result leaves Leipzig third in the table, two points behind Dortmund, who lost 1-0 on Tuesday to leaders Bayern Munich who are seven points clear and on course for an eighth straight German league title.
"Today it (three points) was on a silver platter and we didn't take it," added Nagelsmann.