Hodgson has congratulated Appleton on his first managerial appointment and wished him all the best at Fratton Park.
"We're happy for him but not happy we don't have him anymore," he told Albion's website.
"He deserves his chance and all credit to Portsmouth for coming and finding a guy who was working as an assistant head coach at a Premier League club and going for him. Very often clubs go for men who have managed clubs before and give them another go.
"So, we congratulate them and congratulate Michael on getting the appointment we think he deserves because he is ready to be a manager in his own right.
"It's a big challenge for him but I know it's one he can handle and will do well at.
"The only downside is we lose a good coach and good collaborator that we've been very happy to have working for us."