Arturo Vidal's first leg penalty proved decisive, with a goalless draw at Stade Louis II enough to see Juve through to the final four courtesy of a 1-0 aggregate scoreline.
Having secured a spot in the semi-finals for the first time since 2002-03, Allegri is determined to rediscover the glory days of years gone by in Turin, which is home to two European Cup/Champions League titles.
"Tonight I want to celebrate with the fans - it is turning into a great year for Juventus," Allegri was quoted as saying by UEFA.com. "There were signs of us becoming a great European team again.
"We did not have great games in either leg but Monaco are pretty good - we knew they would be. We did not have many chances but we defended well.
"Monaco produced two big performances, but we had to be brave and we were. It is always difficult reaching the semi-finals but we made it, all credit to our players. We are a group and we gave it our all. Although we did not play a great game, we were ready for every situation and we did what we had to do.
"My players were hit by a virus, they were sick, so we have achieved a big thing by qualifying here. Twelve years on we are in the semi-finals again. I fear no one - we will play the best teams in Europe and this will be a very exciting challenge."
