The former Wales international was dismissed in January and replaced with Paul Lambert, but the Potters' hierarchy have conceded that they should have made a change earlier.
"It is right that supporters will question whether we should have made a managerial change sooner. As a family we are inherently loyal people and this loyalty has served us well in business," said the owners in a statement.
"We will always give people that little bit longer than most to prove themselves and this will continue. However, this does not mean that we always make the correct call and again with hindsight, we perhaps should have made an earlier change.
"Our core focus is now on the future. We are absolutely committed to continue, along with Denise, our significant emotional and financial commitment to this club. We will be doing everything we can to help us secure a return to the top flight of English football as soon as possible.
"We absolutely understand that this is going to be a great challenge and we cannot offer any guarantees. However, please be assured that we will do all we can to work with everybody at the Club to assemble a squad that can make us all proud again."
The Stoke owners have also promised that there will be a "major overhaul" at the bet365 Stadium to help the team mount a strong bid for promotion next season.
The statement raises questions about Lambert's future, given that there is no mention of him in it.