Visiting fans were left tightly packed together outside Elland Road when some of the stadium’s electronic turnstiles stopped working.
Supporters were eventually let in when a gate was opened but many missed kick-off and could not find their allocated seats due to congestion.
Leeds plan to review safety measures at their home ground in conjunction with West Yorkshire Police.
A spokesman for the Newcastle United Supporters Trust said: “The Trust has raised significant concerns to Leeds United in relation to the issues that occurred at the away end at Elland Road on Saturday that could have resulted in serious injury or worse and were not the fault of any match-going Newcastle United fans.
“We have called on those Newcastle fans at the game to get in touch and, so far, we’ve had over 100 fans contact us with their version of events. It appears to be only by luck that nobody was seriously injured.
“No football supporter should go to a match and be in fear of their own safety.
“It is imperative that lessons are learned to prevent this from happening again and it is important that those that caused these issues are held accountable.”
Relegation-threatened Newcastle won 1-0 thanks to a second-half goal form Jonjo Shelvey.
A Leeds 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 Newcastle Supporters Trust, 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.”
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