The 24-year-old battled back from a set and two breaks down in the second to force a decider at Flushing Meadows, but ultimately came up short on a wind-swept night in New York.
"She's a champion," Azarenka told reporters. "She knows what it takes to get there. I know that feeling, too.
"I will not think of how tough is this loss going to reflect on me. I'm just going to take the best out of what happened today, because there are a lot of positive things.
"What's negative is the result. But to see how much you rise to the occasion compared to the other matches, I think it's pretty remarkable."
Azarenka also lost to Williams in last year's final.