Ferdinand watched from the subs bench as Cole set up both West Ham's goals in the 2-2 draw with United in the FA Cup third round on Saturday.
It was Cole's first game for West Ham since re-joining his boyhood club from Liverpool last week.
Ferdinand and Cole duo know each other well, having been products of the Hammers' famed academy before going to play for England together.
"I thought Joe did well," Ferdinand told the London Evening Standard. "Two quality crosses from him and two goals. I'm sure the West Ham supporters will be happy with that.
"I hope the move works out for him. Joe's been plagued with a lot of injuries over the last few years. It's been a bit stop-start for him in recent seasons. It will be good for him and West Ham if he can now play regularly and stay injury-free."
Ferdinand - who has himself been linked with a move back to Upton Park - says only time will tell if Cole made the correct decision in breaking the old 'never go back' rule.
"Everyone is an individual," he said, "and you never know how these things will work out until you try. He's come back to West Ham after a few years and good luck to him.
"Joe looked good and it was a tough cup tie. That's what you expect when you go to West Ham though. It was nothing different to what we anticipated."