The Premier League new boys travelled to The Hawthorns on the back of three straight goalless draws, but their trademark tight defence fell apart, with the opening two scores conceded from corners.
Saido Berahino added two strikes to Craig Dawson's opener before Graham Dorrans compounded Burnley's misery late on.
"It was a performance where we never got started and never got to grips with the game at all," Dyche told Sky Sports. "It was a real low day for us performance-wise.
"There is a reality to it - we've seen other results like this in the Premier League, now one's happened to us it's important we react and learn from it very, very quickly."
Burnley's injury problems worsened, with David Jones and Dean Marney joining Danny Ings, Sam Vokes and Matt Taylor on the sidelines.
"We've handled most of the games quite well, there were a few changes that were forced upon us but it's important that we have a squad that can deal with those changes and we didn't do so well with that today," added Dyche.
"It makes things tougher as the lads have learned to operate with them in the team, but you want players to come in and take their chance.
"Instead, we concede two horrible set-pieces, from our point of view, and then it's uphill from there."