Edinburgh turned down the opportunity to succeed Guy Whittingham at former club Portsmouth a fortnight ago, and Yakubu has said that the players were delighted to see the 43-year-old stay with Newport.
"Words can't really describe how key he's been to the club's development," Yakubu told BBC Sport.
"It doesn't look like it's slowing down any time soon so the longer he can stay here the better. He's done amazing things with this club and it's only natural he's going to attract a lot of clubs and that's just what happens.
"Success breeds more success and the next thing more people want his services. The one thing I've learnt in my career is that good things don't last forever. We're just going to have to make the most of him while we can."
Edinburgh steered the Welsh club to promotion from the Conference last season.