Barrow go down after six seasons in League Two, with a highest finish of eighth two years ago.
Their return to the EFL in 2020 had ended a 48-year spell in non-league, but the Cumbria club will have to regroup quickly before taking their place in the National League next season.
The owners said the club would “come back stronger”, but they also promised that decisions would be made shortly that would start that process.
“We are acutely aware of what’s gone wrong and we are well down the road ensuring the club is heading in the direction we need to go forward and grow,” they said.
“Words are easy to say so let us be judged by our actions. Over the coming days and weeks, we’ll be making a series of announcements as we restructure and fully reset the club.”