The 25-year-old has warned AC Milan of his side's impressive attack and also spoke of his determination to secure a return to the Italian national team
The reigning Russian champions completed the capture of the former Porto and Benfica men for a reported 80 million euros and the Italian is sure that they will improve the team greatly.
"We had a great team and after the last two purchases [Hulk and Witsel] we are competitive enough to win in Europe," Criscito stated to Sky Sport 24.
"We will try to pass through the groups and go further in the Champions League. The attack is of great quality with Hulk, [Aleksandr] Kerzhakov and Danny who will soon return."
Criscito was originally selected in Cesare Prandelli's Italy squad for Euro 2012 but was dropped after being investigated as part of the match-fixing scandal that rocked Italian football.
But the defender now has his eyes on a return to the Azzurri after being cleared of any involvement.
"I think to do well on the field, I started very well with Zenit and hope to be back in the national team but I have not heard from anyone," he added.