Craig Mather resigned his post as chief executive by "mutual consent" last week with non-executive board member Bryan Smart also standing down.
Shackleton said having just two directors was "not suitable" and is trying to find a resolution to the Govan club's boardroom problems.
The latest departures followed those of non-executive director Ian Hart and chairman Walter Smith to leave just two board members of Rangers International in situ - finance director Brian Stockbridge and non-executive director James Easdale.
Mr Shackleton said: "We are actively trying to sort the situation out, we are doing everything we can to get it sorted. It needs stability.
"I have been talking to everybody, trying to map out a path through this minefield.
"Once we have done that I think we can make a decision."