Coast Capital, which has a 9.7 per cent stake in Aberdeen-headquartered First, said the current management team had made several mistakes and "don't know how to manage the business".
James Rasteh, chief investment officer of Coast, told BBC Radio 4's Today programme: "The idea presented by the chairman and the CEO that rather than even attempt to turn around their loss-making UK business, even though it has been their bread and butter for decades... is a clear admission that they don't know how to manage the business.
"We're trying to fix a UK-based business, made up of UK and US-based assets, most of which need turnaround attention, and there isn't a single board member that has prior and proper experience in the industry."
He added that the transport industry is growing, and bosses were wrong to sell off parts of the UK business piece by piece, while keeping large pension deficits on the books.
On Tuesday, a special shareholder meeting is taking place, where Coast will be able to try to replace six board members with seven of its own hand-picked team - most notably led by former transport minister Steven Norris.
One nominee who will not stand for election is David Martin, former chief executive of transport firm Arriva, who failed to submit a so-called "consent" letter showing that he agrees to stand for the board position.
Coast previously said it wants FirstGroup to split its US and UK business and remove itself from Britain's rail industry, where it operates Great Western Railway, South Western Railway (SWR) and TransPennine Express.
But FirstGroup has claimed Coast is "rooted in the past" and simply wants to "seize control of a UK-listed plc without paying a premium".