Cooper, who was born in New Zealand, believes that New Zealand's previous poor record at the tournament, coupled with their hosting the event, has seen the level of expectation on them rise this time around.
"They are supposed to have won this World Cup for the past three tournaments and this is no different," Cooper said.
"A lot of pressure is on them to win this competition on home soil so I am sure they will be worried about how they are going.
"These are the moments you play rugby for, an opportunity to play against the best team in the world in their back yard in a World Cup semi-final."
New Zealand have not won the Webb Ellis trophy since 1987.