Lautaro scored all three goals for Inter as they won 3-0 on the night.
"Today was a very important match for us to win because this way we have a less demanding schedule," Lautaro later told Inter TV. "Fortunately, the team had the right mindset and attitude. I'm happy because we qualified among the top eight teams and that was our main objective.
"I dedicate the ball as a reward for the hat-trick to my son and my family who came here to see me. We closed the game after a quarter of an hour and that happens when you have the right amount of nastiness, with the extra man we then played more calmly.
"I am proud to have reached Mazzola (on 17 goals in the Champions League), but the important thing is that Inter continues to win and I am happy to make the fans happy. We are a great team, we respect everyone and already two years ago in the final we showed our value, last year we deserved to go through with Atletico, but today we want to continue to do well, I am happy with my teammates, the staff and the fans.
"Our goal this year is certainly to win all the competitions we play, now we definitely have to think about a fundamental commitment which is the derby against Milan. This will certainly be a perfect, unforgettable evening. The round of 16 was a fixed objective that we had since the beginning of the season and we achieved it. Missing two games was fundamental for us: we deserved this victory. For me it is a special moment, I feel great, I am playing many games and my body is responding well.
"Now we have to recover because the derby is coming: we know what happened in Riyadh but for us it is not a rematch, all derbies are different and special. Today we celebrate, then we think about the derby which is very important for our path in the championship."