The Welshman has taken control of the team on a temporary basis following the departure of David Moyes earlier in the week, and Evra believes that the 40-year-old has already earned the respect of the dressing room.
"Giggs is a natural," the French defender told the club's official website. "Players like him and Paul Scholes inspire the young players, and the senior players too. This is why they will fight to make sure that Ryan picks them for the team.
"As a person and a player, he instantly gets that respect which is why it wasn't weird to see Ryan Giggs as manager."
Giggs begins his reign by hosting Norwich City at Old Trafford on Saturday afternoon.