The Italian coach is happy with his side's form of late but will not contemplate clawing back into contention for third spot, preferring to focus on the upcoming clash with Pescara
Second-half goals from Mario Yepes, M'Baye Niang and Giampaolo Pazzini sealed the victory, which will now see the San Siro club meet Juventus in the quarter-finals.
"We did not play well in the first period on a technical level. We were very stiff and Reggina made it difficult for us. In the second period we were much better," Allegri was quoted as saying by La Repubblica.
"Juventus? We are now thinking of Pescara, which is more important. We have to recover points we lost earlier in the season. But we do not talk of third place, we have to keep winning as many games as possible."
Niang's goal was his first since his move from Caen during the summer and Allegri applauded the 17-year-old on a special night for the teenager.
"Niang has been doing well and tonight he did well to score. He still has to be given time to grow and I think he has great room for improvement," he added.
Reggina coach Davide Dionigi, who left out several key players for the game, was upbeat despite his side's elimination from the competition.
"We did well against a Milan side almost at full strength. It is a shame because we were better at times in the opening stages. But we are happy with what the guys have done," he praised.
"Our focus is the league, hence why I brought this team. There are many games which do not allow us to play every game with all our best players. I am still pleased with the performance of the players today."