Fans online have claimed there was confusion when entering the ground with a number of tickets being rejected, difficulty moving and families being separated by faulty gates.
One Newcastle fan, Alexander Marshall, posted a long thread on Twitter recounting his experience.
Alexander claimed: " I made it to the front of the pack. My ticket didn't work initially, but after couple of attempts and help from a steward I made it inside. But thats [sic] when things went south. Almost all the turnstiles seemed to fail.
"I was looking back though [sic] at my little sister, a metal gate between us and unrest growing, with nobody doing anything to try and help. It was clear the gates weren't working and people were now stuck and on the verge of being in danger.
"Tempers were rising inside, people asking/shouting at stewards to do something, get someone, fix it. The response was a disgrace. Some in orange just seemed to look through me and others as we pleaded with them to help.
"People, including my younger sister, were getting upset. And with reason. It was scary. All those people and nowhere to go. Nobody doing anything. I was pleading with several people to help, or to get someone that could. Their responses couldn't have been poorer."
Other images that have emerged online appear to show away fans still queuing to enter the ground 15 minutes after kick-off and a turnstile barcode reader falling apart.
Today, Monday, January 24, the reports have been acknowledged by both Leeds United and West Yorkshire Police, as well as Newcastle upon Tyne Central MP Chi Onwurah.
A Leeds United statement read: "The club acknowledges the complaints raised by some Newcastle United supporters regarding issues experienced entering Elland Road on Saturday.
"Leeds United will now work with the NUST, West Yorkshire Police and our own safety team to review the issues raised and ensure we continue to provide a safe environment for everyone attending our stadium. We will not make any further comment until a review is complete."
The West Yorkshire Police said: "We are aware of issues at the Leeds United v Newcastle United game at Elland Road on Saturday that resulted in congestion at the entrance points for away fans.
"We are currently liaising with the club to review the circumstances."
Fans' distress was also acknowledged by MP Chi Onwurah online, who said: "Certainly if any constituent who was there would like to raise that with me please get in touch."
Eddie Howe's side won the fixture 1-0 thanks to a 75th-minute free-kick from midfielder Jonjo Shelvey.
The side's second win of the season saw them climb to 18th in the Premier League, one point ahead of 19th placed Watford and one behind 17th placed Norwich City.