A 2-1 defeat to Paris Saint-Germain in Turin meant Juve become only the second Italian side to lose five of six group stage matches in the competition – after Roma in 2004-05 – though their elimination had already been confirmed.
Juve required a victory to cement their spot in the knockout stages of the Europa League but ultimately must be thankful to Benfica for firing five second-half goals against Maccabi Haifa to prevent the Allegri's side from exiting continental football entirely.
In the Europa League, the Bianconeri will be considered to be among the favourites to go all the way and Allegri has urged his side to use their anger to propel them to better results in UEFA's second-tier club competition.
"We played a good game, it's a shame about the result," he said after the defeat.
"We are in the Europa League, from tomorrow we must turn the page for the championship. We must be angry and immediately resume work and walk.
"On one hand there is reason to be satisfied to have reached the Europa League, on the other hand there is anger for the elimination from the Champions League.
"I'm still very angry and we have to carry this anger inside us in the next games in Europe."
One positive from the defeat to PSG was the return of Federico Chiesa from injury, who had not featured since January, though his recovery will not be rushed," Allegri said.