United made a positive start after going four unbeaten but their new-found belief seemed to evaporate in driving rain and swirling wind on the south coast.
Former United trainee Joshua King struck on the stroke of half-time to claim Bournemouth’s first goal in nearly six hours and give the Cherries their first win since September.
United came into the game in seventh place but now have a haul of 13 points from 11 games – their lowest at this stage of a league campaign since 1986-87 (11).
“If you want to get into the top four you need to win games like this,” said Solskjaer. “It is a step back for us today, but we need to shake it off and go again.”
King, who scored the winner in Bournemouth’s only previous Premier League win against the Red Devils in 2015, was allowed to chest down Adam Smith’s cross into the box before turning Aaron Wan-Bissaka and volleying between David de Gea’s legs from close range.
The Cherries carried that momentum into the second half and Harry Wilson twice went close to doubling their lead, before late substitute Mason Greenwood hit the post moments after coming on for United.
But the visitors could not prevent Bournemouth securing their first win in six, which sent them back above the Red Devils to sixth before the rest of Saturday’s games.