The former Manchester City and Malaga boss pointed out the refereeing decisions during his post-match press conference though he didn't blame the referee for the defeat.
Felipe Anderson had a goal erroneously disallowed for offside in the early exchanges, before Paul Pogba opened the scoring with a penalty following a Robert Snodgrass tackle on Juan Mata that Pellegrini argued was outside the box.
Pogba ditched his previous approach of using an exaggeratedly slow run-up in favour of running up quickly to both penalties and emphatically dispatching them past Lukasz Fabianski. After that, it was not a penalty off Robert - but it was a hard decision.More news: John Legend & Chrissy Teigen squashed by Dwyane Wade during basketball game
Far better to focus on his team's victories in Paris and Turin this season as they attempt to overturn a 1-0 deficit against Barca than make comparisons with Sir Alex Ferguson's men.
'What we did against PSG must give everyone a huge confidence boost because that experience was probably the best those players have had for many years.
"We got away with it, got three points, in a few years no-one will remember how we played if we finished in the top four".More news: Israel's Beresheet spacecraft crashed during attempt to land on the moon
"Of course it's hard, but if you want to be a top team you have to play big Champions League games, and the weekend after it's the Premier League", De Gea said.
The ongoing uncertainty over Ander Herrera's future may have contributed to his ongoing injury problems, Manchester United manager Ole Gunnar Solskjaer has suggested.
"We had the luck today, you always have to take it", Pogba said.
"We played against Manchester Unietd at Old Trafford and it was a good performance but unfortunately we couldn't win".More news: President Erdoğan calls for Sudan to restore peace, democracy
Will Rice leave West Ham in the summer? "I don't know what else I could do". Maybe he was disappointed because he played the first game, which we lost, but I spoke with him the same day and told him he was going to be an important player this season.