Mauricio Pochettino took over the hot seat after Nigel Adkins was given his marching orders despite taking the Saints back to the top flight.
The Italian has one game under his belt and came away from the game with Everton with a commendable point and more importantly, kept a six match unbeaten run going.
Giggs said to Sky Sports: "Everyone was shocked when Nigel Adkins went, but ultimately players have got a job to do. They just get on with it.
"The new manager will put his ideas across and players will just get on with it."
He added: "It will be another tough game for us. Southampton have been in decent form and gave us a good game earlier in the season, so we'll need to play well.
"You want to perform well for your satisfaction and your own form. It also gives you confidence going into the next game."