The defender is ready to make his comeback from injury after missing the Azzurri's first two games, and is confident that they have what it takes to progress
The Azzurri desperately need all three points from Monday's game, but are also reliant on the outcome of the match between Spain and Croatia, as a 2-2 draw would still spell the end of Italy's Euro 2012 ambitions.
Nevertheless, goal difference will be decisive if Croatia and Spain draw 1-1, and Italy then need to win by three clear goals to finish ahead of their rivals.
"We need to win against Ireland first and foremost. We need to win against Ireland, to play well and to show that we have truly arrived," Barzagli told Uefa.com.
"At the end of the game we'll then have to see what the other result is. But, before that, we must concentrate on our own game.
"We have the potential to score three goals as we have great forwards. They can play well and get a feel for the goal.
"When you don't score or when you're losing, it's a problem the whole team has to try and deal with. We have to help [the strikers], we have to create chances and get the ball near the goal.
"The rest of the team will have to help a lot."
Monday's match against Italy and Ireland in Poznan kicks off at 20:45CET.