"It's not beyond us, but I think, without any question of a doubt, we have to win three on the trot now," said Allardyce.
"Unfortunately, we've got Chelsea up next and it's going to be one hell of a result if we can beat them.
"It's going to be a massive task to get anything out of the game the way Chelsea are going at the moment and it would be a real bonus if we could win it.
"We can only try and do our best and hope the gods are with us, that a bit of good fortune comes our way and we can upset them like we upset Arsenal.
"If we can do that, it would be magnificent and it might just kick us on to go into the final two games and win them to keep the pressure on Everton."