Dominic Solanke finished well inside the opening minutes, and was denied a second in the first-half by the woodwork, before Philip Billing and Marcos Senesi both scored with headers after the break to cap a famous victory for the Cherries.
There were boos at half-time and even more at the end of the match, though they were quietened to a degree by the fact so many United fans had made their way out of Old Trafford before the full-time whistle. Ten Hag had no complaints with the reception his players received, as he bemoaned a lack of consistency.
"I understand," the United boss told BBC Sport.
"Disappointed, frustration - we are as well. But we should do better. We have to show it every game, not from one game to another game [having] so big difference in levels."
Victory for United would have lifted them level on points with Manchester City in fourth, and they were expected to fly out of the blocks after seemingly clicking into gear at long last against Chelsea.
Instead it was a sluggish start and one that set the tone, with Andre Onana nearly bringing Solanke down in the box within 60 seconds and the Bournemouth striker then finding space to open the scoring early on inside five minutes.
"The start of the game," Ten Hag responded when asked what went wrong for his side.
"We were not in the right focus. We had a warning shot, almost penalty but then we gave a goal away. The way we conceded it, to us can't happen. Mistake in the build-up, ok, but then we need better positions so they can't so easily come through."
He added: "You have to start right, 100% focus. When you don't, everyone is eager and it can't happen that an opponent is [more] eager than we are."