West Ham United drew 0-0 with Manchester United in their most recent fixture.
West Ham picked up a credible 0-0 draw at Old Trafford at the weekend, but they could have taken all three points back to Upton Park had they been slightly more ruthless.
Zarate was guilty of missing a golden opportunity in the second half of the match, when he put a close-range shot wide of David de Gea’s far post.
And Sullivan said: "Mauro is one of the best finishers at the club and I know he will be gutted that he was not able to convert the chance when he was through on goal.
"Hopefully he will be able to put that behind him and get on the score-sheet when we play Stoke on Saturday."
Zarate is set to receive an extended run in West Ham’s side, following injuries to a number of their attacking talents.
Manuel Lanzini, Dimitri Payet, Diafra Sakho, Victor Moses and Enner Valencia are all on the treatment table at the moment, leaving Slaven Bilic short of forward options.
Zarate had gone into the match against United with confidence, after scoring against West Bromwich Albion the week before, but he was still unable to get on the score-sheet this time round.
Despite his miss, the Argentine has done well to revive his West Ham career this season.
Zarate appeared to be out of favour under former manager Sam Allardyce, but since Bilic has been placed in charge at Upton Park, he has got back into first-team contention, and scored five times so far this campaign.