The Save Our Shirehall (SOS) group was unsuccessful in its bid to get the Abbey Foregate HQ protected from potential demolition.
The council has confirmed it intends to leave the building for a new base, with Shirehall potentially being sold for redevelopment.
Shropshire Council leader Councillor Lezley Picton has said she wants the authority to be out of the building within three years.
The authority has argued it is no longer fit for purpose and would cost too much to bring up to modern standards.
Since the start of the pandemic only a handful of council staff have been working at the building.
A capital strategy from the council has earmarked £27m "linked to the reconfiguration of Pride Hill focussing on a new civic hub".
SOS member Sally Stote said there were concerns over the amount of money involved, particularly after the council paid £51m for Shrewsbury's main shopping centres, one of which it has since closed, with the investment now valued at just £12m.
She said: "This plan is yet a further example of this council's property excess which has seen the £51 million purchase of town centre sites down-valued to just £12 million in just four years."
SOS member John Crowe said the £27m earmarked in the council budget is more than the authority was planning to spend on a previous refurbishment of Shirehall.
He said: "For starters, this £27 million is £3 million more than the Shirehall refurbishment plan of 2018 which was widely seen as way too excessive, and then rejected by the council."
Mr Crowe said the group believes the building is still viable and has repeated his call for the council to abandon its plan to leave the site.
He said: "The SOS Campaign Group maintain that the Shirehall is fundamentally sound. There were 800 staff working there in February 2020, and the sparkle can be put back into our Shirehall for £3 to 5 million and 'future proofed' for safe working.
"The people of Shropshire have the right to question the political motivations and decisions of the present council's leaders that sees significant and excessive spend on a new 'civic hub' when a perfectly sound well-known municipal Shirehall is available for re-occupation and re-use.
“We see this plan as unnecessary and a waste of our council's money. If in agreement, we encourage people to tell their councillors what they think."
Mark Barrow, executive director of economy and place at the council said Shirehall had "failed technically, functionally and economically" and the authority would not be going back on its decision to leave.
He said: "We are dedicated to leaving Shirehall and will not be changing our position on this.
"The original refurbishment scheme agreed by full council was in excess of £20m and that did not include the removal of asbestos.
"Shirehall has failed technically, functionally and economically and of course it’s green credentials are extremely poor.
"What we have witnessed during the pandemic is an acceleration in the way that digital technology enables us to work, which in turn reduces the need for office space considerably.
"The opportunity to work in the town centre also offers much better overall access to public services for the Shropshire public."