On Saturday, the BBC opted to broadcast Strictly Come Dancing from 7.25pm to 9.05pm on BBC One, thus clashing with The X Factor which aired between 8pm and 9.15pm on ITV1.
Speaking to The Times, Sir Michael said that the BBC should not battle ITV for viewers, but instead focus "on the quality and impact of its programmes, not just audience share".
The X Factor beat Strictly in the ratings war, with a peak audience of 10.7 million compared to just 8.7 million for the BBC One show.
Figures released by Sky also indicate that The X Factor was the preferred choice for Sky+ users, with 1.2m saving the ITV1 show to watch later compared to just 686,000 doing so for Strictly.
"Viewers were asked to make a choice between the programmes and that choice didn't go in favour of the BBC," commented Sir Michael.
The chairman also revealed that BBC director general Mark Thompson discussed the row with the Trust during a meeting on September 16, including his explanation that the scheduling conflict was almost unavoidable.