On a freezing night in Turin, Juve dominated last season's beaten finalists Atletico Madrid but failed to even threaten winning by the two-goal margin that would have helped snatch top spot in Group A.
Atletico, beaten 4-1 by city rivals Real Madrid in the final last May, survived a first-half onslaught to hold on for a 0-0 draw and finish top of the group on 13 points.
Juve finished second on ten points, booking their entry to the last 16 for the first time since a quarter-final exit at the hands of eventual winners Bayern Munich in 2013, when Antonio Conte was at the helm.
Allegri, who has moved Juventus away from the 3-5-2 system used by Conte to a more attacking 4-3-1-2, admits meeting Bayern, Chelsea, Real Madrid or Barcelona in the knockout phase is bottom of his Christmas wish list.
"There are three or four teams – Chelsea, Barcelona, Bayern and Real Madrid, for example – who are a cut above the rest," Allegri told reporters after the match
"For now, we're in the last 16 and we'll just see what happens when we get to the draw because we can't change anything."
Juventus lost out on the first-place finish that would have offered a favourable seeding for next week's draw, but after a match in which neither side made a single substitution, Allegri said simply that his side had achieved their aim.
"It would have been good to win with a two-goal margin and finish top of the group, but we've achieved what we set out to do," he added.
"We've had a solid group campaign, let's see now what the draw has in store."
Although Juve took their unbeaten run at home in Europe to ten games, the Italians' failed to score in front of their own fans in Turin for the first time in this group campaign.
Meanwhile, Atletico coach Diego Simeone all but admitted his side had played to defend their lead, and was more than happy with a result which saw them go through as group winners.
"The first half was very intense and we didn't have many opportunities, while in the second we closed down a bit and played on the counter-attack," said the Argentinian.
"We're delighted to finish top of the group, especially given we've only been playing in the Champions League for the past two years."