Hal Robson-Kanu put the Royals in front in the 14th minute before Leroy Lita pulled Boro level with a 29th-minute strike.
Ian Harte and Shane Long both netted braces to secure McDermott's side a well-earned victory, although Lita made the scoreline look a bit more respectable for his side with a 72nd-minute penalty.
Mowbray said: "Right from early on we were under pressure. In the first five minutes we conceded half a dozen corners and it never got much better. Reading have a lot of intensity in their play and their front two work really hard.
"I've been in charge for 19 or 20 games, but it's the first time we have found a performance like that. Even if we have had bad results we've always been in matches.
"This was the first time we have been outfought and outplayed. It's not a day for excuses. We must put it behind us straight away. I would never have thought that we could find that level of performance after the way we played at Nottingham Forest."
Source: PA
Source: PA