This loss was a result of poor effort and some bad breaks (soft goal by Copley, at least three weird bounces that went STL's way). Bad efforts happen. No team gives 100% for all 82 games. It's just reality. Slumps and dud games will occur over the 82 games, regardless of who's coaching.
The CBJ game was far more worrisome in terms of coaching. That was a game where Columbus' system was smothering the Caps, and where the CBJ skaters were playing assertively and confidently in their system while the Capitals couldn't seem to adjust. The Blue Jackets knew where the puck would be and had players positioned correctly to challenge the Capitals in all three zones. The Caps couldn't adjust to get consistent speed through the neutral zone at any point. If you want to draw doom and gloom about the coaching staff, that game is the one to point at.
That being said, that game still doesn't concern me that much. It's one regular season game. It's not a playoff series. Weird match-ups happen. Trotz was certainly outcoached on various nights. Same with Boudreau. Same with every coach in the NHL. You don't always get a ton of time to implement team-specific gameplans during the regular season.