Mr Thompson, who is chairman of OmaghDistrict Council, said it would only have taken 10 minutes for the parade to pass the flags.
BBC: St Patrick's Day parade in Omagh
2.
Sinn Fein councillor Sean Begley - who chaired OmaghDistrict Council's organising committee for the St Patrick's Day celebrations - criticised his unionist colleagues for a "lack of leadership".
BBC: St Patrick's Day parade in Omagh
3.
It's wrong, however, to think these two groups are interchangeable - Omagh, a district with no Alliance councillors, has the highest percentage of people calling themselves "Northern Irish".