Forest boss Steve Cooper said he needed to "bite his tongue" over what he really felt about referee Stuart Attwell and his colleagues.
However, it is understood Forest officials left Old Trafford seething over various decisions they felt were pivotal in deciding the game's outcome.
Attwell sent Forest skipper Joe Worrall off midway through the second half, deeming him to be the last man when he fouled Bruno Fernandes - even though central defensive partner Willy Boly was close by.
The referee then gave a penalty to the home side for a foul by Danilo on Marcus Rashford, which many felt was extremely harsh on the visitors. Fernandes subsequently scored what turned out to be the winner from the spot.
Video Assistant Referee (VAR) Robert Jones checked both decisions but agreed with Attwell's on-field calls.
Forest will decide within the next 24 hours whether to go directly to PGMOL, which is already in the spotlight over Mike Dean's admission that he failed to instruct Anthony Taylor to review Marc Cucurella having his hair pulled during Chelsea's London derby with Tottenham last season because he was "a mate".
After Saturday's game, which Forest led 2-0 after four minutes, Cooper said: "In games like this you need things to be how they should. I am not going to talk too much as I don't want to get into trouble but I was surprised how quickly the decisions were made.
"You just bite your tongue in terms of what [you] really feel but of course they were defining moments."
-- Courtesy of BBC Sport