The Bianconeri were dumped out in the group stage of last season's tournament but the Italy defender has taken great encouragement out of Atletico Madrid's campaign.
The Rojiblancos do not have anything like the same budget as the likes of Barcelona and Real Madrid, yet they managed to reach the final of the Champions League and win La Liga.
"Not getting out of the group last year represented a huge disappointment," Barzagli told JTV's 'Filo Diretto'. "Now we're hoping to do better and at least get through to the next round.
"It will not be easy. The Champions League is tough and the gap between the top European clubs remains, given the investment that they have made.
"We're not on the same level but we can follow the example of Atletico Madrid, who were a minute from being champions of Europe last season. Therefore, we can also dream."
While Juventus have struggled in Europe, they have had no such problems in Italy and are currently bidding to win a fourth successive Serie A title.
However, even though the Bianconeri opened with a 1-0 win at Chievo, Barzagli is taking nothing for granted, particularly having watched last season's runners-up, Roma, kick off their 2014-15 campaign with a 2-0 defeat of Fiorentina.
"Roma is fresh from a great campaign and they have already had a good result," the defender mused. "They're the most formidable opponent.
"Inter have signed experienced players. Napoli also had a good transfer market.
"Milan can do well with Inzaghi and they have strengthened the squad a little.
"Lazio also had a great market, so we cannot underestimate anyone."
Barzagli, who joined Juve from Wolfsburg in 2011, is currently out injured but is expected to return to action in October.