The winger, who started the game at the Stadio Olimpico on Tuesday night, admitted that it was not always easy going against the Ukrainian champions - even after Edin Dzeko scored the night's only goal to ensure an away goals triumph.
Roma will find out their last-eight opponents on Friday.
“On a psychological level, it was a very difficult game,” Perotti said. “We knew how good they were and we were also aware that we had to score but not concede because otherwise it would have been tough.
“But ultimately, we’ve been dreaming of an evening like this since after the first leg over there: it was tough at times, but ultimately the fans ended up happy while we were exhausted. It was the best thing that could have happened.
He added: “We had to score, but it was more important not to concede. We know that we create a couple of chances every game, and usually we score, but when we concede, we get nervous, lose our heads and start flooding forwards, everyone trying to score.
“We spoke about how we had over 90 minutes to score and we needn’t lose our heads. I think we played with more intelligence than in other matches.
“We were fortunate that Edin scored a difficult goal: I think that was the only place he could have put it. Then we defended like animals. I think we put in the right performance.”
Perotti was full of praise for the two teammates that created that crucial goal, revealing that the dynamics of the strike - Edin Dzeko timing his run to latch onto Kevin Strootman's astute pass - was something that the side works on diligently in training.
“First you need to have the quality that Kevin has, and then Edin’s timing to stay onside,” Perotti said. “There were moments in the first half when Cengiz or I could have waited a moment to stay onside, but you really want to make that run; instead you need to stay cool-headed.
“It’s something we work on a lot in training, ever since the coach arrived. It’s great when you see the results of what you do in the week.”
After that, it was a matter of staying calm under pressure.
“When you get to moments like these in games, it’s your mentality that is fundamental,” he said. “That’s what makes you run more even when you’re dead on your feet and can’t make the pass. It was a game that we couldn’t lose, draw or concede in. I think we all put in an amazing effort because we knew that getting to the quarter-finals after the poor couple of months we had was fundamental for us and the fans.
“If we get Juventus in the quarters, we’ll try to win. It doesn’t matter if it’s Juve or Barcelona, at this stage all seven other clubs are strong. They’ll be difficult ties. But we mustn’t think about that just yet, let’s enjoy this moment and start focusing on who we’ve drawn tomorrow in April.”
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