"It was a new system and we weren't really used to it", Mbappe said.
Paul Pogba picked up a red card just as injury time was starting for a second yellow card that will be a blow for any chance of a comeback in the away leg in three weeks time.
Solskjaer, who had won 10 of his 11 games in charge before this clash, admitted his team were a step below the French champions.
United made a highly aggressive start to the game, but too often, their forwards chose the wrong option or failed to deliver the right pass, although Marcus Rashford and Pogba both tested PSG's 41-year-old keeper Gianluigi Buffon with near post shots.
"Marco and Marquinhos are incredible, but you can not play all season with just two midfielders - not at a club like PSG or a Bayern Munich".
"We are going to have to go down there, believe in ourselves, play a good game and improve from today obviously".
"Slip up in those fixtures, lose ground on the top four and there will be doubts as to whether Solskjaer is the man to challenge Liverpool and Manchester City for the title next season".
Coach Thomas Tuchel praised Di Maria - a £59.7m flop during his one season at United - for brushing off the jeers of the home fans, and claimed that Ashley Young should have received a second booking for shoving his old team-mate into the perimeter wall.
No club has ever recovered from losing the first leg of a Champions League tie by two goals or more and still progressed.
"I was watching with Noah and we said "wow, that's a tough challenge", said Solskjaer on Monday.
"We are happy, but it's only half-time in the tie and we need to continue preparing well, because I think in the last 20 minutes we dropped off a bit physically".
"In my opinion he needs to play with a good mindset, be positive and realise it's part of his development".
"Don't give him that space to go into, but he's lightning quick of course".