Allegri was worried his side could lose their cool as they trailed 2-0 from the first leg but his fears were unfounded.
"The boys read the game in the best possible way, playing at a high tempo and exploiting the width of the pitch," he said.
"I wanted to us play like that also in the first leg, but then I changed something and it didn't go the right way.
"It was a fluid, cool and calm performance. We had been waiting for this evening for a long time and we risked having a frenetic game, instead we had to pressure them whilst also keeping a balance, and we did it.”
His opposite number Diego Simeone, who had set his team up to defend their lead, had no complaints about the result.
"Juventus were better and deserved to win the game. They pushed us back," he said.
"You must congratulate opponents when they play a game like that and you are beaten like today. We made many mistakes, for sure, but I mean me not the players. They were better tactically and on second balls. That is why they won the game."
The Argentine added: "It wasn't about commitment, work rate or effort... they beat us because they were better and when that happens, all you can do is take your hat off, work harder and draw conclusions."
(Writing by Brian Homewood; editing by Ken Ferris)
