After an even but uneventful first 20 minutes, Etienne Capoue put the visitors ahead from distance at Molineux, before the Hornets doubled their lead immediately afterwards through Roberto Pereyra.
After conceding just a single goal in five league games, giving away two in the space of just 58 seconds gave Wolves a mountain to climb, admitted Coady.
"It's the second goal that killed us really," the captain explained. "It's not like us - we usually manage the game pretty well, but they say that you're always vulnerable when you've just scored or just conceded, and so it proved today.
"At 1-0 you're always in the game, but at 2-0 down it becomes a struggle. Watford are a good side and they can hold on to a two-goal lead.
"It's disappointing from our point of view - we weren't really at the races in the first half. We lost our shape; they dragged us out a little bit. We weren't good enough - we weren't close enough to players and we weren't pressing well enough, and we got punished for it.
"The Premier League is such a tough division. We've seen today that if you're off the pace for a little bit, teams get after you and the punish you. Watford are a good side and they've done that to us today."
The defeat brought to an end a run of six league matches unbeaten for Wolves, who made a habit of bouncing back strongly from their rare defeats in the Championship last season.
Their only other league loss this campaign - against Leicester - was followed by a hugely encouraging, deserved draw against champions Manchester City, and Coady says that the hard work will start immediately as the squad look to get the Watford defeat out of their system.
"Every team is very, very good in the Premier League," he continued. "If we play like we did today, we'll concede goals - it's as simple as that. Today wasn't good enough, so we've got to come back in on Monday and go again.
"The manager needs a reaction. We've been beaten - we don't like it but it happens. We've got Brighton away next weekend and that now becomes a huge game for us - we've got to put a lot of things right.
"You're always hoping and willing to get better, whether you win, lose or draw. We'll all come back in on Monday and look where we went wrong, improve our shape and look to improve the way that we play."