Wales are still looking for their first win of the autumn Test series following defeats to Argentina, Samoa and New Zealand.
Tomorrow's match is Wales’s last at the Millennium Stadium and Cuthbert wants his side to bow out with a bang by upsetting the Aussies.
“This is a big game for us and we know we can beat Australia,” said Cuthbert, whose side have lost their last six games.
Defeat would more than just hurt Welsh pride. Warren Gatland’s team would fall outside the top eight in the International Rugby Board rankings if Australia storm the Welsh capital, and be in the third tier of seeds for the 2015 World Cup draw.
However Cuthbert concedes that it is difficult to find chinks in the Australians’ armour. “I don’t think Australia have any weaknesses and they are all world-class players,” said Cuthbert.
“We just have to have a big collective effort, play our game and have discipline, which cost us in the summer, and if we do that, we can get the win.”