Ramsey will join the Turin giants on a free transfer in the summer upon the expiration of his Gunners contract, having agreed a lucrative move on Monday.
“I'm still fuming at the fact that we're going to lose him," Seaman told talkSPORT.
“What's more frustrating is they've announced that Emery is going to get £40 million to spend in the summer, that's how what you'd have to pay to get someone like Ramsey anyway.
"It's demoralising for me and even more demoralising for the fans to hear that and then to see quality players leaving again.
“I don't get what the forward thinking is. Emery gets one transfer window and is told he can only get loans, then in the second window told he only has £40m to spend.
"It's so frustrating."