A midweek victory over Chelsea had offered cause for optimism but in-form Bournemouth exposed just how far Ten Hag's United have fallen this season.
The Dutch coach looked forlorn as he watched on in the teaming Old Trafford rain as his shambolic side were comprehensively outplayed and fortunate not to lose by more.
Bournemouth's fans taunted Ten Hag with chants of "You're getting sacked in the morning" while home fans booed loudly at the final whistle although many had long since trudged off.
United's fourth home league defeat of the season failed to inspire much hope ahead of next week's must-win game against Bayern Munich in the Champions League.
Manchester United have struggled to find consistency in their performances this season.
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"You've got to be at your best in every game, starting with focus. When you start like we did, you get killed," Ten Hag said. "They are good opponents but we have to do better. I've got to take responsibility for it.
"I understand fans are disappointed, frustrated. We all are but we should do better and we have to show it every game, not to have so big levels from one game to another."
After a shaky start to the season the south coast club are now thriving under head coach Andoni Iraola's high-pressing style and their relegation fears are rapidly receding.
They took the lead after five minutes when Lewis Cook burst through the United defence and squared the ball for Solanke to finish tidily.
Solanke was close to making it 2-0 before halftime when Cook again played him through but this time his shot struck the post.
But United were floored by two goals in five minutes for Bournemouth -- Billing and Senesi both scoring with thumping headers from Marcus Tavernier deliveries, as United's defence went AWOL.
Bournemouth hunted for more goals and were denied a very late fourth when Dango Ouattara bundled through and netted but his effort was ruled out for handball after a VAR check.
Bournemouth's victory did not flatter them and the club are up to the relative safety of 13th place. For sixth-placed United it remains one step forward and two steps back as they undid all the good work of Wednesday's impressive victory over Chelsea.
Ten Hag's team have now lost 11 of their 23 games in all competitions this season.