Both the Scottish FA and SPFL said they are "astonished" that MSPs backed proposals to give fans the right to buy their clubs.
Green MSP Alison Johnstone's amendments to the Community Empowerment Bill received unanimous support by the Local Government Committee.
"We are astonished by the impractical and unworkable amendments put forward by the Scottish Green Party," a joint statement said.
"We will consider our position."
Johnstone told the committee that agreeing to the changes would turn the legislation into a landmark bill.
If passed by the full parliament, supporters' trusts would get "first refusal" when a club comes up for sale.
A supporters' trust with a registered interest in a football club would also have the right to buy shares in that club, including a controlling interest, at any point.
However, the SFA and SPFL feel the proposals could undermine their own efforts to increase supporter involvement in clubs if the Bill is passed by the full Scottish Parliament at its final stage later this year.
A joint statement from the two bodies read: "The Scottish football authorities, in conjunction with sportscotland and Supporters Direct Scotland, have been involved in the Working Group on Supporter Involvement in Football Clubs since April 2014.
"This group was convened by Shona Robison MSP, Cabinet Secretary for Health, Wellbeing and Sport, to provide meaningful, practical recommendations aimed at enhancing supporter involvement in their local clubs.
"These discussions - involving senior managers of the Scottish FA and Scottish Professional Football League - culminated in a series of proposals published on January 30th, with the intention to facilitate and cultivate improved supporter involvement. This included a clear statement that 'a legislative approach was not considered desirable or necessary at this stage'.
"We are astonished, therefore, by the impractical and unworkable amendments put forward by the Scottish Green Party - and approved by the Scottish Parliament earlier today - which effectively disregard almost a year of constructive partnership by all organisations represented on the working group.
"We will consider our position along with our working group colleagues in early course."