The 35-year-old Seppi, 10 years older than Edmund, hung in for a while as balls kept coming back harder than he hit them, but fell short in his bid for a first title since 2012.
"The reasons you get to right now and the trophy here and what makes it nice is because you have to experience all those downs and then it makes you realize that [you] just can't take the success for granted," Edmund said.
"You get the success from having the downs because you learn from that, and the low points mentally and the disappointments of losing matches, those help you get to the happy times, the success, the winning the matches."
Edmund won five straight games to take the first set and build a big lead in the second, seizing control with shots that seemed to get more powerful as the match went on.