The Dark Blues sit bottom of the table, nine points adrift of Ross County and having played a game more than their nearest rivals.
Irvine, stand-in skipper after Stephen O'Donnell was ruled out for the rest of the campaign, knows most people expect a quick return to the First Division for Barry Smith's men.
And he wants Dundee to use the fact they have been written off as motivation for staging an SPL comeback in the second half of the season.
The defender said: "It's us against the world, especially with everyone writing us off. But we have put ourselves in this position.
"It comes down to togetherness in the squad. We need everyone pulling in the same direction.
"We're in a tough situation here but some of the squad have experienced it at this club before.
"We've seen the tough times and come through them. We can do it again."