The Scot took charge of the Red Devils in 1986, but by January 1990 had failed to win any silverware, with his side enduring a seven-match winless run.
The FA Cup Third Round paired United with former European Cup winners Nottingham Forest at the City Ground, with many believing a win for Brian Clough's side would ensure Ferguson the sack.
However, Robins' goal settled the tie in the visitors' favour, with further wins over Hereford, Newcastle, Sheffield United, Oldham and Crystal Palace handing them the trophy.
Robins, now manager of United's League Cup opponents Barnsley, recently joked that Ferguson had never thanked him for saving his job.
However, the 67-year-old has responded by saying that, while that particular goal was important, it was not a defining moment.
"The goal at Forest was an important goal, don't get me wrong, and who's to say what would have happened without it, but I don't think it saved my job," he said in The Telegraph.
"You never know in football. Who's to say how the club would have reacted if we'd lost and if crowds had tumbled?
"One thing's for sure though. [Director] Bobby Charlton would not have let it happen. He knows better than anyone the heartbeat of this football club.
"This football club needed the foundation of youth and we were doing some great work on that side of it. Bobby knew we were on the right road."
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
