The statement comes after Di Canio criticised the club's prospective new owners for selling Matt Richie to fellow League One promotion-chasers Bournemouth without consulting the Italian.
Di Canio said he would review his position at the County Ground on Friday, prompting the club to issue the following statement on their official website: "The decisions made over the course of the last few days have not been made lightly, and in the case of the decision to sell Matt Ritchie, have been done in conjunction with the new owners.
"Whilst the Board understands Paolo's desire to gain promotion and is wholly supportive of this, the Board's considerations and responsibilities extend beyond the on-field activities of the team.
"On some occasions it is faced with difficult choices and whilst we recognise the disappointment to all caused by the sale of Matt, the Board has not shirked its duty to face up to the harsh realities of its financial situation.
"We look forward to the swift resolution of these short-term issues, Football League approval of the new owners and hopefully a win against Crawley."The former West Ham, Sheffield Wednesday and Celtic striker is set to take charge of the Robins' game against Crawley on Saturday.
Di Canio took the Swindon job in May 2011 and led the team to promotion from League Two in his first full campaign.