United finished fifth in the Premier League that season, missing Champions League qualification to City on goal difference despite both clubs collecting 66 points.
Van Gaal was dismissed just 48 hours after guiding the Red Devils to FA Cup glory, with Jose Mourinho subsequently replacing him.
The 75-year-old Dutchman believes City's alleged financial irregularities unfairly affected the competition and ultimately cost him his job.
City have faced allegations concerning sponsorship arrangements and financial reporting between 2009 and 2018.
"For me, at the time, missing out on the Champions League in 2016 was probably the deciding factor in my dismissal from Manchester United," Van Gaal told The Athletic.
"And all the consequences and suffering this entailed.
"I cannot turn back history now. Not even the English Football Association can do that."