Marcus Rashford's 94th-minute penalty at the Parc des Princes gave United a 3-1 win in France to send the English club through on away goals after becoming the first team in the competition's history to overturn a 2-0 home defeat, AFP reported.
"I'm stunned. I haven't been able to sleep," Mbappe told TF1 in an interview. "It's difficult, we'd worked so hard to get to this point and we're disappointed. We're going to try and pick ourselves back up."
PSG's game at Nantes this weekend was postponed although it remains well clear of second-placed Lille and all but assured a sixth Ligue 1 title in seven seasons.
Thomas Tuchel's men are also through to the last four of the French Cup, but Mbappe admitted it was hard to look ahead to rest of the season with the pain of last Wednesday's defeat still raw.
"Honestly, it's hard to give it too much thought because the Champions League was our goal. The stadium was full for a magnificent occasion, we spoiled the party. We didn't want to ruin it but in the end we did."
However, the 20-year-old allayed any fears among PSG fans that his immediate future could lie elsewhere in the wake of the club's latest European failure.
"I think I will be here, that's guaranteed even," he said.
"With this elimination and all the problems it's going to create, there's no point in my personal situation being added to it. So there, that's clear and precise."