Beckham admits they had to raise £10m to save the club after learning of the situation from former Manchester United teammate and fellow investor Gary Neville.
He told the Athletic: "I very rarely panic but when Gary came to me and said ‘OK, this is the situation, we need to find a way of saving the club’, I was concerned.
“For him more than anyone, because Gary committed to Salford from day one.
"I’ve spent a lot of time there but I know what it means to him. I know what the people in the club mean to him. I know what the fans mean to him.
"For him to say, ‘we need to sort this out’… He very rarely burdens me with anything, so I knew this was something we had to fix."
The new owners were able to bring in £20-30m in the allotted time to rescue the League Two strugglers.
Beckham also said: "When we reached that, Gary got really emotional. That’s what it means to him and it’s the passion you want.
"If we hadn’t have done it, the club would have been in serious trouble.”