After a 1-0 home win in the quarter-final, first leg, the Bianconeri held firm for the goalless stalemate that ensured they reached the last four of Europe's premier club competition for the first time since 2003.
"It was an important game tonight. Some players were under tremendous pressure because it had been 12 years, and we were the favourites," Juve defender Patrice Evra told BeIN Sport.
"We qualified Italian style. It's ugly but it's solid and it's efficient."
Monaco had the better chances and the most influential player in Geoffrey Kondogbia while Juventus sat back and waited for the perfect opportunity to counter.
While that never arrived, their rock-solid rearguard ensured they did enough to make it through.
The result, however, left a bitter taste in the mouth of Monaco defender Aymen Abdennour.
"We defended well, today we played a great game, we deserved to score at least a goal," he said
"It was 50-50, really. In the first leg we also had a lot of chances but we could not convert them. Today on the pitch, Monaco were better than Juventus."
Abdennour hopes Monaco, third in France's Ligue 1, can quickly bounce back on the domestic stage, so that they can play in the Champions League again next season.
"We must turn the page and focus on the league. We will try to finish third and why not second," he said.
Evra added that he felt this Monaco team reminded him of the one he played for from 2002-06, which reached the Champions League final in 2004.
That season, Monaco knocked out Real Madrid and Chelsea en route to the final where they eventually lost to Jose Mourinho's Porto.
"Their run this season reminded me a bit of our run back then," the former France defender said.
"I'm happy tonight but I feel for them."
Monaco coach Leonardo Jardim, however, said his side had demonstrated what they are capable of.
"We were not inferior, we showed Europe the good work of our team," he said.
(Writing by Julien Pretot; Editing by Toby Davis)
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