Although missing leading striker Etey Shechter through a leg injury, Hapoel forwards Toto Tamuz and Ben Sahar created a number of chances but failed to convert.
Frantic defending by the home team ensured that Hapoel gained their first point in the group stages but that was not enough to lift them off the bottom of the standings.
"We played an excellent game today and the fact we feel we missed out speaks for itself. We had so many chances and did not score. It is disappointing," Hapoel coach Eli Guttman told reporters.
"I am proud of my players. They gave everything and deserve full credit."
While Schalke keeper Manuel Neuer made a number of acrobatic saves to frustrate Hapoel, at the other end Nigerian international goalkeeper Vincent Enyeama enjoyed a drama free evening as he was rarely threatened by strikers Raul Gonzalez and Klaas-Jan Huntelaar.
Schalke stayed in the hunt to progress from the group with seven points. They trail leaders Olympique Lyon by two points and Benfica have six.
"Today's game was harder than I had anticipated," Schalke coach Felix Magath said. "They played well and I am pleased with the point we gained."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.