The 57-year-old businesswoman sold her 15.9 percent stake in the club in April 2011 to allow the American to embark on a full takeover.
Bracewell-Smith’s outburst comes in the wake of Arsenal’s loss to League Two outfit Bradford City in the Capital One Cup - the latest disappointing result after the club’s worst start to a Premier League season in manager Arsene Wenger’s 16 years in charge.
When asked about her thoughts on Kroenke’s reign, Bracewell-Smith said on Twitter: "Disappointed would be an understatement! Shows he cares very little. Why he wanted to be part of AFC [Arsenal] I do not know.
"If making money was the motivating factor, surely there are better ways. Football is a business of passion and SK [Kroenke] has no passion for AFC."
Bracewell-Smith then re-tweeted a message from another follower which implied that herself and other former shareholders would not have sold their stake in the club if the now-deceased former owner Danny Fiszman was still in control – while another hinted at the businesswoman being “convinced” to sell.