Mies and his partner, junior Daniel Cochrane, also were eliminated in the quarter-finals of the doubles competition.
The No. 11 seed, Sebastian Fanselow of Pepperdine, defeated No. 19 Mies 7-5, 3-6, 6-4 in a match played indoors due to bad weather. Mies finished with a 21-10 record in singles during his senior season.
Mies and Cochrane, who are ranked No. 6 nationally in doubles, fell to the No. 2 team in straight sets on Saturday evening. Henrique Cunha and Raphael Hemmeler of Duke took a 6-2, 6-3 victory vs. the AU pair.
It was a great tournament for us," Auburn head coach Eric Shore said. "These guys did a great job, and I'm happy for both of them, but I know they're disappointed. I think if we had played a little better today, we could have done more.
"Andy had his chances (in singles), he was up 3-1 in the third. He played well and put himself in a position to win, just didn't close the deal. But he played well this week, and I'm proud of him. It was a nice way to finish his career at Auburn this week in this tournament.
"Dan's going to be a senior next year and hopefully can build on this," Shore added.
The Auburn pair made school history at the tournament at the University of Ilinois. Prior to the event the Tigers had never sent a singles player and a double team into the NCAA Men's Tennis Championship quarter-finals in the same season.