Former United trainee Josh King scored a 54th- minute winner to prevent United from bouncing back from their mid-week Champions League exit at Wolfsburg and keep them three points off the pace in the Premier League.
“It is always like that. It is not new. It is a matter of belief,” the Dutchman said.
“Believe in the manager or not. That is the most important thing. Last year the fans all showed their belief and that is the most important thing.
“But for me the most important thing is the commitment of my players to perform as we have agreed and I can only tell you they want to do that.”
United fell behind after precisely 100 seconds when Junior Stanislas’s wind-assisted corner from the left deceived visiting goalkeeper David de Gea and curled straight into the net.
Marouane Fellaini equalised in the 24th minute, but King exploited inattentive defending at a corner to tuck away what proved to be the decisive goal.
It was Bournemouth’s second successive impressive win, following last weekend’s 1-0 success at Chelsea, and sent them up to 14th place in the table.