Liverpool manager Juergen Klopp after the match
The Reds boss sent the French international home this week after reportedly growing concerned by his attitude during their preparations for the new season.
Watford v Liverpool - Barclays Premier League
The decision surprised some, especially given that the Reds have several lingering issues regarding their defence ahead of next season.
It has led to questions about whether the manager was right to send the player home, but Barnes has insisted that the decision was a correct one.
"Managers needs to be given that autonomy,” he told the Daily Star.
"The manager needs to be given that strength to then say if 'I take a decision to drop somebody or to send them home or tell someone off then you will have to back me' - and the fans do.”
Liverpool's Mamadou Sakho and Christian Benteke in the stands
It now remains to be seen if Sakho - who joined the club from Paris Saint-Germain in 2013 - has a future at Anfield after this latest incident.
Last season, it would have been surprising to find him out of the first team given how poor the Reds were in that area of the team.
They have added both Joel Matip and Ragnar Klavan in that position this summer though, meaning Klopp has more options available to him ahead of next season.
He has already shown his ruthlessness in sending him home, and it would not be surprising to see Sakho moved on at some point.
Liverpool manager Juergen Klopp