The motion was put forward by Emma Jacobs, a student at the University, in a forum where students proposed ideas on how to make their union better.
Only ten of the fifteen (67%) student panel members voted for the motion and the union's rules dictate that should less than 75% of the panel vote yes or no to a motion, it must then proceed to a campus-wide referendum.
Miss Jacobs was calling for LUU to do more to combat antisemitism on campus.
She asked for the union to adopt the International Holocaust Remembrance Alliance (IHRA) working definition of antisemitism and implement a multifaceted approach to combat discrimination.
In the motion Miss Jacobs explained: "Across the UK, there has been an increase in antisemitism on campuses, including swastikas, 'Hitler was right' stickers, and issues of antisemitism within student societies."
She continued: "As a campus with one of the largest Jewish student populations in the UK, LUU must ensure that Jewish students can feel safe on campus and are free to fully express their Jewish identities without fear."
The motion asked that the union ensure Sabbatical Officers have training on issues affecting Jewish students, hold at least one Holocaust Memorial Day event per year and run awareness and educational events around issues of antisemitism.
The IHRA definition specifies eleven "contemporary examples of antisemitism", some of which prompted debate in the LUU student panel.
In a statement, the University's Union said: "A panel of 15 students voted on student-proposed ideas around how to make their Union better. One idea considered was ‘Should LUU do more to combat antisemitism?’ which included the suggestion to adopt the IHRA definition of antisemitism and its full examples.
"At the forum, every student agreed antisemitism was unacceptable. However, there was debate both for and against adopting all of the examples listed with the IHRA definition.
"Within our democratic system, 75% of the student panel have to vote yes for an idea to pass or no for it to fail. If an idea does not get 75%, it may proceed to a campus-wide referendum.
"In this case, 10 students voted for the idea and 5 students voted against it, 12 votes were required for the idea to pass or fail. The next step is to take the idea to referendum, should the proposer wish to."
After the vote Emma Jacobs tweeted her disappointment and said that she had felt intimidated by other students in the room.
She said: "When I put forward this motion to Leeds University Union vote, I didn’t expect to spend over an hour being sniggered at when I said I wouldn’t withdraw a motion to combat antisemitism. I’m disappointed. It’s exhausting being a Jewish student and I wouldn’t wish this on any other group.
"I barely slept last night. I cannot stop thinking of the injustice of how this motion was approached by the vast crowd who turned up to intimidate me (attempting) to get me to withdraw. Why’s the Jewish community the only one who aren’t allowed to define our own oppression?"
Leeds Jewish Society, JSOC, said in a statement: "We are incredibly disappointed that a motion on LUU combating antisemitism did not pass tonight.
"This means that every University of Leeds student has the right to vote on this matter.
"This means, in theory, that LUU could be giving money to students to run a campaign against combating antisemitism.
"We will not cower. Jewish students have a right to feel safe on campus."
A University of Leeds spokesperson said: “Every student on the Better Union panel was clear that antisemitism is wholly unacceptable. The disagreement was about the formal definition of antisemitism.
“The University is committed to promoting and positively encouraging free debate – including the definition of antisemitism – and we are confident that we have a robust and consistent policy on freedom of expression.
"The University would take firm and decisive action against any members of the University demonstrating antisemitism or other forms of hate crime.”
However, Labour MP for Leeds North East Fabian Hamilton tweeted his support to Jewish students and concerns over the result of the motion.
He said: "I am extremely concerned that a motion proposing that Leeds University Union should combat antisemitism was not agreed earlier this week. Leeds University prides itself on its diversity and it's hugely disappointing that this will now be put to a campus-wide referendum.
"Jewish students should be supported and made to feel safe, not only on the university campus, but across the city and throughout our country."