The Serie A champions played out a 0-0 draw with Spanish counterparts Atletico Madrid in Turin on Tuesday and the point was enough to secure second in Group A.
It marks a return to the last 16 for Juve, who were eliminated at the group stages in the 2013-14 Champions League campaign.
Head coach Allegri believes there are four teams that are currently a cut above the rest in Europe's premier competition, but feels that his side are capable of competing with the elite.
"[Finishing second] means Juve will take on one of the group winners in the next phase of the competition," he told Sky Sport Italia.
"The level of European teams is three or four who are far above the rest - Bayern Munich, Barcelona, Real Madrid and Chelsea.
"The rest of us are battling and we are aware of our qualities.
"We can slowly improve our self-confidence and I think we have played a good group with undeserved away defeats in Athens [against Olympiacos] and Madrid."
