"Firstly I think the guys put in a fantastic performanc," Allegri said.
"The changes made a difference and gave us a real boost, it was the right time because I felt there had been a bit of dip in the physicality of the Spurs players. Even at 1-0 down we had a good reaction and we carried on playing, we knew we were capable of scoring and if anything we were concerned that we would concede another goal.
"You are going to find certain games that are really tough. We did suffer, but that's normal in football. We worked on possession a great deal and that was important to us."
Juve are into the last eight of the competition for the third consecutive season, where they will join Liverpool, Manchester City and Real Madrid. The other four spots will be decided next week.
"First and foremost we are really happy we won tonight and are through to the last eight. There are some really good teams in the last eight," he continued. "We are happy with what happened tonight but we need to go away and start thinking about our next game.
"We are having a good season, we are in the final of the Coppa Italia, doing well in the league and through to the next round of the Champions League. Who knows, anything can happen in the Champions League."