Accies came back from 2-0 down following the first leg to beat Terry Butcher's side 4-3 on penalties at Easter Road and seal their return to the Scottish Premiership.
But Frenchman Andreu - who scored a last-gasp equaliser to send the match into extra-time - believes the angry groans coming from the Leith stands terrified the confidence-stricken home players.
He said: "After the first leg they were confident but we knew if we got the first goal they would crumble.
"Their fans were on their backs but you can accept that because football is their life.
"But for Hibs you could see it was hard for them because they were scared. That is normal because they have not had a great season and have had a lot of injuries.
"I think they are good players but they were just under so much pressure. With the fans reacting so angrily all the time, it is hard. Even more so when you are not confident.
"Every player can give the ball away but when the fans yell at you it makes it harder to perform."
Jason Cummings had put Hibs two up with a double at New Douglas Park last Wednesday but Jason Scotland cut the deficit in half with an early strike in the Edinburgh return.
Andreu then levelled the game in the third minute of stoppage time after Jason Scotland wriggled clear in the box before Kevin Thomson and Cummings saw spot-kicks saved by Accies number one Kevin Cuthbert in the shoot-out.
But Andreu - one of four Hamilton players to successfully convert from 12 yards - admits he feared he had blown his big moment as they game ticked towards full-time.
"It has been amazing - I still can't believe it," said the 26-year-old. "We never panicked. I still thought we would score, even when the game was going into stoppage time.
"I was glad that Jason gave me the ball because there had been two situations before where he could have but didn't see me. Thankfully, this time he did.
"I knew I had to put my shot on target. I managed to put it wide of the goalie but it was heading for the defender and I thought, 'Oh no'.
"But it was a 'meg' and went through his legs and that's when I went wild."
The play-off success earns Accies a return to the top flight three years after being relegated and Andreu says boss Alex Neil already has the basis of squad which can compete in the Premiership.
"I think we should maybe add some more experience players but we have a really good team already and have showed that this season," he said.
"We didn't expect to get promoted at the start of the season but after every game we started to believe.
"We have some really young players like Louis Longridge and Ali Crawford but we know it will be hard going up a level.
"However, we want to compete and show we can compete in the top league."