The Parisians had a 2-0 lead going into the second leg of their last-16 tie at Parc des Princes but suffered a 3-1 defeat, enabling Ole Gunnar Solskjaer's side to progress on away goals.
PSG dominated possession with 73 per cent and equalled the Reds' tally of four shots on target, but their fate was sealed when Marcus Rashford netted from the spot in the fourth minute of stoppage time.
"The game we played was unforgivable," Marquinhos told reporters after the game. "We have to analyse, think and we have to be men. It's a difficult moment.
"We had to give everything on the pitch. Now it's over, we cannot say 'You had to do that, you had to do this'.
"These are still details, and it's always the case at the high level. I think it's a good time not to talk too much. As we say in Brazil, it's time to eat our own sh*t.
"It's a sh***y moment and we have to keep working."
Marquinhos was the only PSG player available to talk to journalists in the mixed zone after the last-minute defeat.
Captain Thiago Silva had earlier asked fans for forgiveness on television following the performance and said the side must now focus on Ligue 1.
They currently hold a 17-point lead over second-placed Lille, and are set to face Nantes in the semi-finals of the Coupe de France. But crashing out of the Champions League will be bitterly disappointing for the French outfit as their quest to be crowned European champions continues.
Manchester United, on the other hand, will now wait to see who they draw in the quarter-finals after Solskjaer reinforced his candidacy for the permanent managerial job with the Red Devils.
They next face Arsenal in the Premier League on Sunday.