Bournemouth ends goal drought with 1-0 win over Man United
Bournemouth climbed above midtable United with the win, which was sealed by Joshua King's strike shortly before halftime — his club's first goal since September.
After United missed chances to level in an even second half, Solskjaer suggested his squad hadn't been good enough to compete.
"I thought the response second half, at least we went for it," said Solskjaer.
"We didn't stop trying but it was the lack of quality that couldn't give us the point or three.
"We need a response because games like this you need to win if you want to challenge for the top four and today we're disappointed."
United's defense was slow to react again in the 74th, when De Gea dived at full stretch to push Harry Wilson's shot wide.
United surged forward in the final 10 minutes but couldn't come closer than Mason Greenwood hitting the post in the 83rd. Shortly after, goalkeeper Aaron Ramsdale showed good reactions to save a shot from Scott McTominay.
Defeat in pouring rain on England's south coast ended a recent resurgence for United. It had won its last three games, but has now also failed to win five of its last six league games.
United is three points behind Bournemouth.
King's strike was Bournemouth's first league goal since the 2-2 draw with West Ham on Sept. 28. The Cherries are looking to recover some of their strong early-season form after a five-game winless run in all competitions.