Manager Jose Mourinho branded the defending in the first half at the Vitality Stadium "awful" while regular centre-backs Smalling and Victor Lindelof have had to deal with their share of criticism from some supporters.
He added: "There's so many good things to come from the game".
United have had their issues this season in the Premier League, although shoots of recovery are starting to appear.
Buoyed by what Mourinho called "calm" words at the interval, United was a transformed team in the second period and several times went close to scoring.
"In the second half I knew by having the two brothers on the bench - Rashford and Lingard - I knew the brothers could come in and make an impact", the Portuguese manager said after the game, as reported by Manchester Evening News.
The win for United means they are now level on 20 points with Bournemouth, and are four games unbeaten in the Premier League, following a less-than-convincing start to the season. "We are going to be in a better position", he said.
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"We were really poor, defensively terrible".
And just when the game seemed to be heading to a stalemate, Marcus Rashford scored the victor from close range in the injury time to seal all three points for the Red Devils. The team was much better and we created lots of chances.
"I can't believe how bad we started". Now it seems that they can't do without the French winger, who scored in his fourth straight Premier League appearance against Bournemouth. Things need to be set-up off you.
Mourinho has spoken of striving to find the right balance to a team which has developed significant defensive vulnerabilities, and Herrera's performance showed he has a further option as he attempts to establish that balance and his strongest XI. The lead can be overturned against teams like Newcastle and Bournemouth, but big games are coming thick and fast and United need to be ready for them from the first minute.
Mourinho's side will now switch their focus to the Champions League following a return of four points from their opening three games.
Manchester United travelled to Bournemouth on Saturday knowing that a defeat would have left them six points behind their overperforming hosts.