Indian badminton players knocked out of All England doubles
After losing the first game 21-16, Rankireddy and Shetty took the second by a convincing score of 21-11, only for the Danes to prevail 21-17 in the decider.
The match was given added spice by the fact Denmark's Mathias Boe is now the Indian team's doubles coach.
But Astrup said that Boe's presence "didn't affect us in any way".
"It was a great game –- a very mental game for all of us on court," he told the Badminton World Federation website.
The Danes will now play French brothers Toma Junior Popov and Christo Popov in the quarterfinals.
All the seeds in the women's singles got through comfortably to the last eight, with India's PV Sindhu too strong for Line Christophersen as she defeated the young Dane 21-8, 21-8.