Manchester United manager Ole Gunnar Solskjaer said it was a "step back for us" as his side's three-match winning run ended at Bournemouth.
"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."
Bournemouth manager Eddie Howe: "Today we were much more like ourselves with the ball and also very determined without the ball.
"We managed to keep three clean sheets in a row so I am really pleased with that and the attacking play was back today so I think we fully deserved to win.
"These results could be season defining. In our previous Premier League campaigns we have beaten top teams and we know what these results can do for our confidence in the longer term."