Royals made three bids for the Icelandic midfielder on deadline day, with the last believed to be in the region of £10million.
However, Tottenham Hotspur were not willing to sell the 23-year-old, who is well known to McDermott after coming up through the Royals academy.
"It was unfortunate," said the Reading manager. "We were here until late and thought we were going to get a deal done.
"We made three good offers and I have to thank the owner for his support on that, unfortunately we couldn't get it over the line. We thought we had a real chance but Gylf is a Tottenham player and a very good one at that.
"They didn't want to sell him, that's it. If a club wants to buy someone and the other club doesn't want to sell, fundamentally it came down to that. Like Gary Hooper at Celtic, they didn't want to sell him. We thought Tottenham had an interest at one point but not in the end."
Sigurdsson would have been Reading's fifth signing of the window after Daniel Carrico, Hope Akpan, Stephen Kelly and Nick Blackman.
He would also have been by far the most expensive if they had managed to secure his services for a club-record fee.
"It would have been a great present for our fans and that's what Anton (Zingarevich, club owner) tried to do," said McDermott.
"Unfortunately we couldn't get it over the line, but this shows we can compete at another level. We can do our research with players from lower leagues and we've done it successfully, but also to compete for Gylfi was fantastic, it wasn't quite to be."
Royals will be looking to continue their fine start to the year when they host Sunderland tomorrow (Saturday, 3pm ko).