The pair came together on Monday, with experienced midfielder Morrison apologising for hitting young striker Berahino for reportedly refusing to apologise for a mistake that led to Cardiff's late equaliser in last Saturday's 3-3 stalemate.
The Baggies boss said: "They solved the situation between themselves in a perfectly natural manner almost as if they were two brothers from the same family.
"I spoke to Saido - he perhaps seems to be more responsible than other people of his age and I told him that I trust him and trust that he will continue to work well."
The club declined to confirm whether either player had faced disciplinary action.
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