Most of the inflation appeared to come from a mix of massive fiscal stimulus and supply chains that got blown up by the pandemic, so large increases in demand coupled with decreased capacity to supply, driving up pricing for capacity.
Arguably increases in some asset prices could be attributed to QE, but the story doesn't really hold water for CPI ex-housing.
As an aside, I don't even think this course of events was a mistake. It was much better to have some inflation from huge stimulus but avert economic disaster, and then deal with the inflation through the relief valve of higher interest rates. There is no relief valve for total demand destruction.