France midfielder Pogba scored nine times last season but failed to live up to his then world-record £89m fee, following his return from Juventus to United last summer.
Matic's £40m capture is now expected to free up more of Pogba's attacking instincts which can only bode well for the Red Devils, according to Giggs.
The Old Trafford legend said: "I expect Pogba will improve a lot this season. He's been back a year now and the introduction of Matic is a good buy because it frees him up.
"That's what you want to see from Pogba, getting on the end of crosses and scoring goals."
Giggs, speaking at the FA and McDonald's Community Awards, added: "I think Pogba is capable of dropping deep or playing in an old-fashioned midfield two and I expect him to be more effective this year.
"He managed nine goals last year and hit the crossbar and post plenty of times as well, so he can bring the goals that might turn draws into wins and have a real effect on the team."