Sir Alex Ferguson racked up 38 trophies during his legendary time in charge at United, leaving Moyes with a tough act to follow.
But Giggs, who has played over 1,000 matches for club and country, sees no reason why there should be any change as he prepares for his 24th season at Old Trafford.
"I think it is a challenge and as a player you always want challenges," said Giggs.
"First and foremost, there are great players there and we have just won the league, so everything is in place for it to carry it on."
The former Wales international is currently attending the FIFA U20 World Cup in Turkey as part of his UEFA Pro Licence course and admits his attention is turning to what he will do when he finishes playing.
Giggs, who signed a new one-year deal in March, said: "I have got to start thinking that it is near the end. I have to start thinking about what I am going to do afterwards.
"I am in the process of doing that and obviously coming on this course has helped me - speaking to other people, listening to what the coaches or tutors say, and just trying to get little bits that can help you.
"Everyone has their own style and everyone picks up different things. Obviously, I'd be stupid not to pick up on the stuff I've learnt from Sir Alex.
"I don't know whether I am going to be a coach or a manager, if I decide to go into coaching, but it is obviously exciting for me. I have been playing for 20-odd years and it is a new chapter in my life."