The Scot succeeded Sir Alex Ferguson as the United manager in the summer, and after initially struggling has now found his footing.
Moyes led the Red Devils to their biggest away win in the Champions League in over 50 years as his players beat Bayer Leverkusen 5-0 in Germany to book their place in the last 16 of the competition.
"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," Beckham told Sky Sports News.
"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."
United are currently sixth in the league table with 21 points from 12 matches, seven points behind leaders Arsenal.