Hillsborough match commander David Duckenfield claimed a gate to the stadium had been “forced”, a former FA official told a retrial.
Glen Kirton went to the police control box shortly after the 1989 FA Cup semi-final was stopped.
Mr Duckenfield was heard to say “there had been an inrush of supporters”, he told Preston Crown Court.
Mr Duckenfield, 75, denies the gross negligence manslaughter of 95 Liverpool fans.
Under the law at the time there can be no prosecution for the death of the 96th victim, Anthony Bland, as he died more than a year and a day after his injuries were caused.
Mr Kirton, the FA’s head of external affairs at the time, told the jury he had seen fans being “hauled” into the stand above the terraces and climbing perimeter fences minutes after the match between Liverpool and Nottingham Forest kicked off.
About 10 minutes after the match was stopped at 15:06, he and FA chief executive Graham Kelly spoke to Mr Duckenfield, who was a chief superintendent at the time, he said.
Mr Duckenfield pointed to a monitor in the control box and told Mr Kelly that a “gate had been forced, and there’d been an inrush of spectators.”
The jury has previously been told that Mr Duckenfield admitted the comment was a lie, when giving evidence at the inquests into the deaths of 96 supporters.
The court was shown footage of Mr Kirton at the side of the pitch at about 14:40 with Sheffield Wednesday club secretary Graham Mackrell.
He said: “Graham volunteered to me that there were large numbers of people still to come into the ground.
“I think the figure he used was something like 20,000.
“Looking around the ground I couldn’t quite see where 20,000 people would go.”
The trial continues.