It was "immediately apparent" that Burt had suffered a serious head injury, he said.
Security staff and students tried to resuscitate her but she died soon after.
The victim has not yet been formally identified and a post-mortem examination is due to take place on Thursday afternoon.
Distressed witnesses there was "complete chaos" outside the club and "blood everywhere" after the barrier "toppled over".
He added: "Those students close to her have lost a wonderful friend, whom in their shock they grieve for, alongside her family and friends". There was a metal barrier that they put at the front to stop people coming in.
A fellow student, who was in the queue at the same time, told the Guardian they were "completely at the mercy of the crowd" during the crush that led to a barrier collapsing next to Burt. There were two lots of people in just one queue.
"Many people were sobbing, guys and girls, and everyone was hugging each other and making sure their friends were okay".
One told the Northern Echo: "People were barging to get in. My friend said he knew she was not going to make it out alive".
TRIBUTES were last night paid to a high-flying student who died in a crushing incident outside a nightclub.
Witnesses said that there were about 600 people inside the club in the city. The queue has gone around the fence and as they pushed to get in it caused the fence to fall over.
"The girl was trapped under the fence and crushed".
He said: "There was a fair bit of panic". The back of the club was being protected by the bouncers so people were sitting on the steps at the side in small and large groups, all coming to terms with things they had seen.
Olivia Burt, 20, who was in her first year at Durham University, died from a serious head injury following a crowd surge believed to have started when a group pushed into the 100-strong queue, according to witnesses.
'My thoughts are with Olivia's family and friends, may you rest in peace'.
Missoula is described as a smart chain pub with a cocktail list, a classic British menu and uncluttered contemporary decor online.
Olivia sustained fatal head injuries while queuing to enter Missoula club at 11.50pm on Wednesday Night.
A Durham Constabulary spokesman said: "Officers are investigating the death of a student".
"You will appreciate that I am unable to share further details given the ongoing Police investigation".
'Our thoughts are with the young lady's family and friends'.