He praised the majority of fans for their support, as well as head coach Fabian Hurzeler and the players for their commitment.
The Albion deputy chairman shared his thoughts in the programme notes for the 2-1 win over Bournemouth.
Barber wrote: “Fabian, his staff and players deserve a lot of credit for our recent results, but even more so for ensuring they stayed entirely focused by ignoring so much of the nonsense on social media following a couple of tough results.
“Quite how anyone thinks rash judgments, idle rumours or, at times, abusive comments help is beyond all of us.
“While reasonable opinions, comment and different points of view are part and parcel of the entirely legitimate daily rituals of our national sport, unfettered abusive comment from a tiny minority on social media continues to be an issue that needs better control and greater sanction, particularly when it is intimidatory or threatening in any way.
“Thankfully, as we saw with the fantastic support we received from our fans at the Amex for the nest two matches against Chelsea – where the atmosphere was first-class for both games – and at Southampton this past weekend, the overwhelming majority of fans go out of their way, and at considerable personal expense, to support the team in all situations and regardless of the odd disappointing result.”