Ministers can call in council proposals to close schools and ultimately reverse the decision if they think the proposal will be to the detriment of the community.
However, this has left ministers open to accusations of bias if there is a perception that they could gain party-political advantage from the veto.
Mr Russell was himself accused of intervening in school closures in Argyll and Bute in 2010 when he was vying to become an MSP the following year.
The Government has now secured an amendment to the Children and Young People Bill that would defer the decision to new school closure review panels.
Ministers will retain the right to call in decisions and appoint the panel convener, leading to concerns that ministers can "play to the gallery" by calling in controversial closures but "divert responsibility for making unpopular decisions".
Mr Russell said: "Establishing the school closure review panels will improve transparency and remove allegations of political bias from the process."
Liberal Democrat MSP Liam McArthur said: "I have concerns about ministers retaining the power to call in council decisions but leaving examination and determination to the panel of experts.
"This leaves ministers free to play to the gallery by calling in controversial decisions but without having to worry about actually determining whether or not the decision was justified."
Labour MSP Neil Bibby said: "There appears to be an attempt to divert responsibility for making unpopular decisions to the panel and it is unclear who the panel will be accountable to."