The Baggies were knocked out of the Carabao Cup after Louie Sibley scored the only goal of the game to help Derby into the third round of the competition.
Callum Robinson and Matt Phillips both missed good chances as the Championship side fell to their second competitive defeat of the season.
Speaking after the match Bruce, who made 10 changes for the cup clash, said: "When I look back now, have we done enough to win it? I'm not so sure. We knew it was a bit of a gamble from me to play as many kids and also the players who needed to play.
"It was in the back of my mind that you run that risk but I still think we created enough chances. We didn't particularly play great but we should have been two up in the first three minutes.
"The frustration for me is that we're sloppy, we're not clinical enough and it niggles away at me constantly because we've created enough."
Derby interim manager Liam Rosenior saw his side extend their unbeaten run to five matches in all competitions.
He said: "I couldn't be prouder of the group, the young players that came in and showed their quality and spirit against what is an outstanding team.
"What pleased me most was the energy and commitment. We had to work really hard against some top players but what I was so impressed with was how brave they were."