United endured a shaky start under David Moyes but have since started to climb the Premier League table and on Wednesday booked their place in the knock-out round of the Champions League with a game to spare.
The 5-0 romp over Bayer Leverkusen was United's biggest away win in Europe for over half-a-century, but Beckham was not surprised by the result.
The 38-year-old told Sky Sports that the transitional period since Sir Alex Ferguson handed over the reins at Old Trafford is over.
"I don't think it was a game changer because I think we've seen over the past few weeks that players are performing and players are gelling together, there's more confidence in the team. You can see that and you can feel that.
"David Moyes is a great manager he's had success with Everton over the years, the way they played the game, the way they had that togetherness.
"I've known David for quite a few years when we played together at Preston, I know how driven he is, I know how loved he is by the players and he'll have success.
"There was always going to be that transitional period of Sir Alex Ferguson leaving but like Sir Alex always said, 'Manchester United is Manchester United'.
"Big players leave and the club moves on and it's the same with the manager. He'll always remain part of Manchester United in such a huge, huge way but David Moyes is the manager now and you can see the players coming together."