The 2-0 defeat saw Villa miss Champions League qualification, with the visitors aggrieved over Morgan Rogers being denied a goal to open the scoring.
Rogers had appeared to nick the ball away from United goalkeeper Altay Bayindir before scoring in an empty net. However, referee Thomas Bramall, aged 35, had blown for a foul before the ball had passed the goalline.
And as Bramall had stopped play before the ball entered the net, the video assistant referee (VAR) could not intervene.
Villa director of football Damian Vidagany said in the aftermath: "We are going to send a complaint.
"The complaint is not about the decision, it is about the selection of the referee - one of the most inexperienced referees in the Premier League.
"It's not about the decision, clearly it was a mistake. The complaint is about the referee. The problem is why the international referees were not here today."
Aston Villa statement
Villa's complaint reads: "Aston Villa can confirm the club has written to the PGMOL to raise concerns over the selection process of match officials following today’s game with Manchester United at Old Trafford.
"With such high stakes surrounding today’s fixture, the club believe a more experienced referee should have been appointed. Of the 10 referees to officiate across the Premier League today, Mr. Bramall was the 2nd least experienced.
"The decision to disallow Morgan Rogers’ goal, which would have given the club a 1-0 lead with 17 minutes remaining in the match, was a major contributing factor to the club not qualifying for the Champions League.
"As per the standards that have been established over the course of the season, a decision to whistle early is clearly inconsistent with current refereeing guidelines. VAR exists to ensure that these types of situations receive the scrutiny they deserve. Unfortunately, the technology was not allowed to serve its purpose.
"Ultimately, we acknowledge that the outcome for us will not change, but we believe that it is important to address the selection methodology to ensure that high stakes matches are treated as such with regards to officiating and to ensure that the implemented VAR technology is allowed to be effective."